"Whilst" and "While" are actually interchangeable when it comes to conjunctions...
> "While" can be used as a conjunction, a verb, and a noun. Its meaning changes when its function changes. "Whilst", on the other hand, is just a conjunction (If I am not wrong). In other words, both can used as a substitute for "although".
(ex: While/Whilst Anna preferred walking on the beach, John preferred a walk in the park.)
> "While" as a verb is actually something new to me!
(ex: He whiled the deathly hours away until she came back home.) "Whilst", however, cannot be used here, as it is strictly used as a conjunction!
> "While" as a noun is pretty common.
(ex: I only slept for a while last night because I needed to wake up early.) This is different from "awhile", who only acts as an adverb. (so you'd say "...slept awhile last night...")
Because "whilst" is only a conjunction, it wouldn't fit here either.
> "While" as a conjunction is also very common.
(ex: Tina played her favourite game, Flappy Bird, while she was waiting.)
In this case, "while" can be replaced with "whilst".
(ex: Tina played her favourite game, Flappy Bird, whilst she was waiting.)
The doubt between these two words is because "whilst" is seemingly more archaic, and used less often. (I, on the other hand, tend to use "whilst" quite a lot, be it on paper or real life! I think it's a beautiful word.)
So, that being said... "Whilst" is ONLY used as a conjunction (part of speech that connects phrases, clauses, or words), and "while" can be used as a noun (person, place, thing, idea), a verb (action word), and a conjunction!