Both when and while can be used to talk about actions or situations that take place at the same time.
Swan identifies the following differences:
We can use both words to introduce a longer 'background' action or situation, which is/was going on when something else happens/happened.
|Somebody broke into the house when they were playing cards.|
|While they were playing cards, somebody broke into the house.|
Note that when and while clauses can go at the beginning or end of sentences.
2 Simultaneous long actions
We usually use while to say that two longer actions or situations go / went on at the same time.
|While you were reading the paper, I was working.|
If we are talking about ages and periods of life, we use when:
|When I was a child we lived in London (NOT While I was a child …)|
|His parents died when he was twelve (NOT … while he was twelve)|
3 Simultaneous short actions
We can use (just) when to say that two short actions or events happen / happened at the same time:
|I thought of it (just) when you opened your mouth.|
While is not possible in this situation.
4 Reduced clauses
It is often possible to leave out subject + be after when and while:
|While/When in Germany, he got to know a family of musicians. (=While/When he was in Germany …)|
Practical English Usage, Michael Swan, OUP, pp. 73-74
While vs whilst
There is no difference in meaning between these two words. In British English whilst is considered to be a more formal and literary word than while.