Is there a guideline to distinguish between the two? They seem to mean the same but I am sure they don't.
1 When you see the colour red, you should stop walking.
1a When you see a red colour, you should stop walking.
2 I want the room to be the color white.
2a I want the room to be a white color.
Language is not always consistent and it isn't always exact. This being said, it is at the very least commendable to strive for exactness. This is perhaps the gist of many of the comments here.
When you see a red colour ...
If you want to express seeing a traffic light, you probably should say "when you see a red (traffic) light". But maybe you want to say "if you see anything red": a traffic light, but also a "don't enter"-sign (no 267) a red line on the floor or whatever, then stop walking. In this case "if you see something red" would be better.
Of course "a red colour" does exist, but then "colour" is a synonym for "shade". "Mauve", "russet", "carmine" and "blood-red" are all "red colours". But this is perhaps not the meaning you intended.
2 I want the room to be the color white.
2a I want the room to be a white color.
Again, language is neither consistent nor exact. If you want the room to be white you probably mean you want the walls to be white, maybe the furniture too. In 2a "colour" again means "shade". What exactly the - grammatical - difference between "off-white" and "white" is, so that of these two
I want the room to be an off-white colour
and
I want the room to be a white colour
one were to be correct and the other weren't eludes me. Of course, "white is white" (which is, btw., not the absence of colour - that would be black - but the presence of all colours), but then "red is red" and we have established above that there are several variations on that one. The same is true for white. The RAL-catalogue for instance, lists RAL9001, RAL9002, RAL9010, RAL9012, RAL9016 and RAL9018 all under "weiß".
Then, on the other hand, there is some leeway in expression: "to be pedantic", when one says "I want to watch a movie" it is implied that one doesn't only want to watch but also to listen (silent films today are the very rare exceptions) to it. Would we correct him? Probably not.
In general (philosophical rant ON): language is a device to transmit meaning. As long as this is done with a sufficient success-rate you are doing right. By making your language more clear, more concise and more exact (in other words: the better you speak/write a language) you will increase this rate of success and therefore you should undergo every possible effort to do so. On the other hand, there is leeway and as long as you are "sufficiently successful" in transporting the intended meaning you are doing OK. (philosohpical rant OFF)
At first blush, this question appeared to be a duplicate of What is the difference? a or the? However, the specific use of color makes the question colloquially different.
Here in the U.S., few people would ever use the examples you propose. Far more commonly, I will hear:
When you see red, you should stop walking.
I want the room to be white.
The use of the articles "a" and "the" can make the examples confusing, but let's start with an explanation where they can be used clearly: the paint industry.
I want the room to be a white color.
This would refer to any of the two dozen or more shades of white that are available to the customer, including the basic white. A variety of colors may be used to tint the basic white, but the tinting is so light that the color is still very much white.1
I want the room to be the white color.
This would be a very odd way to state the desire, but it makes perfect sense in the paint industry where pre-tinted cans of "white" or "bright white" paint exist. Usually only one such can is available within a selection of paint under one brand.
But those forms would only be used if we required the precision, which in my experience, is almost never
Even in the case of people asking for paint, the most precise form in my area is usually:
I want the room to be white.
This can refer to either:
And that last statement is really important
It's permissible in English to express an idea without caring about the details. A great many assumptions may be made or details ignored because they're not important enough to require precision.
When I speak of "a precise use of language," I'm referring to the effort to be absolutely clear. There is no ambiguity about what is said. Lawyers strive for this noble state of linguistic perfection — but it's whomping difficult to attain and it's very rare for its use to matter.2
The truth of our reality is that someone might not actually know what they want or even know that there's a choice. Worse, the speaker may skip over context because, to them, what they're talking about is obvious. In a great many cases, the customer might simply ask...
I want white.
Because how the paint will be used is irrelevant, or they believe it's irrelevant, often forcing the store clerk to ask for additional information because all paint is not equal. But the speaker frequently doesn't know that.
Therefore, the form of the sentence has as much to do with the speaker's ignorance of the subject as it may the listener's ignorance. I do not use "ignorance" in a negative way, only to refer to the fact that there are often details in any conversation that are unknown until someone starts asking questions.
An answer to your question...
If we ignore grammar and consider only how someone might colloquially express the ideas, there is no difference between your examples. I.E., "the color red" and "a red color" have the same contextual meaning. You'd sound funny to a native English speaker, but the listener would understand what you meant.
If we embrace a bit of grammar, there are differences... but those differences also require context.
If we entirely embrace grammar, you (the speaker) are required to enumerate the entirety of your context. You can't leave anything out.
When you see the pedestrian control signal that controls crossing the street you wish to cross glow Pantone 187 red, which is used in the United States, rather than Pantone 342 green, which is also used in the United States, or the traffic control signal controlling the flow of traffic traveling parallel to the path you're walking glow the previously identified color of red rather than the previously identified color of green, or the traffic signal controlling the flow of traffic traveling perpendicular to the path you're walking glow that same color of green rather than that same color of red, you should stop walking before you step over the curb of the sidewalk and onto the street, which would endanger your life.
Keep in mind, the odds of that last statement successfully including the entirety of context aren't simply bad — it's guaranteed. There is a reason we embrace a certain ambiguity in language.
Generally, people can figure out what we're talking about, which is why you'll betimes note that we drop the use of articles.
Can't I just have white paint?
1 For the benefit of the reader: white (and black) in the paint industry is a pigment like any other. Untinted paint in its pure form (there are complications here that we'll ignore) has no color. If applied to a surface, it will dry clear. Thus, white is not the presence of all colors (such as you see on your computer screen) or the presence of too much color (such as you see when looking at the sun or a bright light regardless the light's color) and black is not the absence of color. Curiously, when you mix equal amounts of all the available pigments, what you get is a muddy brown.
2 That's a global statement that would be difficult to defend without this footnote. Compared to all spoken language on the planet over all of time, the need for absolute precision is, indeed, very rare. On the other hand, there are situations where precision is very much required. The technical trades are the simplest example, which is why there's a difference between technical writing and many other forms or intent of writing. So, I beg of you, don't stress too much over my global claim.
It's the normal difference between "a" and "the", being that "a" refers to "one among many", and "the" refers to a specific one.
We think about colour words sometimes as distinct colours, and sometimes as ranges of colour. So if you say "a red colour", it means something like, one of the range of colours called "red". On the other hand, "the colour red", means that exact colour, as if there's only one colour called "red". We know this isn't strictly true, but it's overwhelmingly the normal way to talk about colour. We almost only refer to ranges of colour when we're talking about art and design.
So to your example sentences, (1) and (1a) mean the same thing, but (1a) sounds odd because it's not a context where the particular type of red matters. (2) means a pure white, while (2a) includes colours near white because the context is interior design.
