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But you can't find anything while you're crying.
But you can't find anything when you're crying.
I'll tell you about it while Frank saddles the horse.
I'll tell you about it when Frank saddles the horse.
When should I use when, and when while?
Are these sentences correct?
When used to mean "during the time that something is happening," while is synonym of when.
While I was waiting at the bus stop, three buses went by in the opposite direction.
All the sentences you wrote are correct.
The main difference between these two words is that when usually means at or immediately after some specific point in time, whereas while always means during some [usually, extended] period of time.
Thus, for example, if we take an activity often considered so quick it happens at a "point in time"...
You should cover your mouth when sneezing. (3460 hits in Google Books)
You should cover your mouth while sneezing. (131 hits)
...but if we take an activity that lasts [a lot!] longer...
You should not smoke while pregnant. (2940 hits)
You should not smoke when pregnant. (137 hits)
...the when/while preference reverses. Without more context (how long/how often do you cry?), there's nothing to choose between OP's first two examples. While would be more likely if you're crying right now, but either would probably be accepted in most contexts.
Also note that in...
He opened the door when I knocked
He opened the door while I knocked
...the when version means immediately after (a perfectly normal situation). The while version forces you to imagine some unlikely contrived context where the knocking and the opening are taking place at the same time. Thus in OP's second pair of examples...
1: while always means I'll tell you at the same time as Frank saddles the horse
2: when strongly implies I won't tell you until [after] Frank starts/finishes saddling the horse
...where in #2 only the specific context distinguishes whether the intention is to start telling at the same time as Frank starts saddling, or [immediately] after he's finished.
Finally, note that when can often be paraphrased as on any of various occasions when, whereas while may be used to mean during the one and only timespan when something is happening.
In the context that you gave, While means "during the time that something is happening"; When means "at the time that something happens".
In the first pair of sentences, because the action of "crying" is generally understood to last for some time, the distinction is minimal; the words can be used interchangeably.
In the second pair of sentences, there is a difference in meaning. Using while focuses on the actual time spent doing the saddling, and using when focuses on the point at which the saddling action starts. Therefore, if you use while, my understanding is that the saddling has already started, you are going to tell me something right now, and you will be able to tell me most or all of it before the saddling is complete. If you use When, my understanding is that the saddling will begin at some point in the future, and that point is the point at which you will tell me something.
X when Y or when Y, X means that if Y happens, X happens. Y will be the start of something or an event that doesn't have a duration.
X while Y or while Y, X means that for the duration of Y happening, X happens. Y will be a continuous activity or something that has a duration.
