While thinking about the nuances between "in" and "inside", I also started thinking about the nuances between "out" and "outside" (prompted by considering the expression "going out" after thinking about the difference between "I'm staying in tonight." vs. "I'm staying inside tonight.")
What I've come up with is that "inside" and "outside" are compound words (perhaps a more knowledgeable linguist could expound on this idea) that denotes the location of the something being described with respect to the "sides" of something, sort of like
indoors, outdoors; inwards, outwards
or even better (from M-W online),
in·sid·er noun (ˌ)in-ˈsī-dər, ˈin-ˌ\
: a person who belongs to a group or organization and has special knowledge about it
out·sid·er noun \ˌau̇t-ˈsī-dər, ˈau̇t-ˌ\
: a person who does not belong to or is not accepted as part of a particular group or organization
: a person or animal that is not expected to win a race or competition
The noun "insides" also tends to be quite literal, referring to the parts/components on the interior of something or, alternatively, the innards of an animal. (Neither the online M-W nor Am.Herit. define "insides" separately from "inside").
"In" and "out", however, because they lack this "qualifier" (if you can call it that) have over time become associated with various expressions and are generally much more idiomatic than their counterparts, which as the following examples show, are read rather literally when used.
Bob came in today. vs. Bob came inside today.
The latter carries the sense that Bob came indoors, whereas the former tends to be associated more closely with the expression "came in to/for work".
I'd also like to note that if you apply the "ejaculated" definition to "came", the "inside" form would be the more appropriate one to use.
The doctor is out. vs. The doctor is outside.
The "out" in the former signifies that the doctor is not currently available because he isn't present in the office and carries no connotations about where the doctor is relative to the office; it also reminds one of the expressions "out of the office" and "out of town".
The "outside" in the latter, at least to me, reads very similarly to "outside" as in "just outside the door" and "just outside the office". It seems to imply that the doctor is very close by, but isn't actually inside.
I'm staying in tonight. vs. I'm staying inside tonight.
I went out every day last week. vs. I went outside every day last week.
The expression "staying in" implies that one is not "going out", in the sense of, say, "going out to the bars", "going out on a date" or "going out to party". The "inside" and "outside" versions, however, are rather literal and are counters, respectively, to being "outside" and "inside" one's own home.
I'm eating in tonight. vs. I'm eating inside tonight.
The former implies that one is staying at home to eat - perhaps by ordering take-out or cooking for oneself; the expression has no indication about this - whereas the latter simply implies that one is eating indoors as opposed to outdoors, perhaps in the sense that instead of dining on one's terrace as one usually would, dinner will happen in the dining room.
I'm ordering in tonight. vs. I'm ordering inside tonight.
The former implies that one is staying at home tonight instead of going out to eat, and that instead of cooking, he's ordering take-out to be delivered to his doorstep. The latter implies that - at least in the context of dining (although it is a rather unique and uncommon situation) - instead of placing one's order outside the restaurant as one usually might, the intention tonight is to place the order inside the restaurant.
He's in town this week. vs. He's inside town this week.
He's out of town this week. vs. He's outside of town this week.
In each pair, the former is fairly common and is also the only appropriate way to say the expression. Although grammatically correct, there is no possible context or situation in which the latter would make sense (technically, in conversation, were "town" a proper noun, the latter expressions would be 'more' correct, although the "inside town" sentence would still be illogical).
I want in on the bet. vs. I want inside on the bet.
I want out of the bet. vs. I want outside of the bet.
Again, in each pair, only the first works. The latter expressions, as in the previous example, are not idiomatically acceptable.
Context: Imagine an oversized object, exactly one side of which is red, being moved into a house with a front entrance through which the object likely will not fit. The following sentences are being said to someone in the vicinity and aware that the object will be or is being moved indoors but cannot see exactly what is going on and knows nothing more.
The red side is in. vs. The red side is inside.
The former might be something you yell to indicate that whoever is moving the object just succesfully managed to get the red side of the object through the doorway, almost like a progress report of sorts. The latter, however, is a more cut-and-dried description and describes the state of the couch at some point in time while the red side is inside the house; it's something you might say when telling the story, as in "so picture it - the red side is inside the house, Jake's outside with a flamingo on his head...".