"Do you want to try the fish?"
Translation:Vil dere prøve fisken?
Is the difference clearer if you think of them as "to test/taste" and "to attempt" instead?
"Å prøve" has two main definitions:
1: to test, try, control, investigate (alt. verbs: "å teste" (I, II), "å kontrollere"(III), "å undersøke" (IIII))
"Vi har [prøvd/testet] [/ut] det nye kurset."
"We've [tested/tried out] the new course."
"Har du [prøvd/smakt] fisken?"
"Have you [tried/tasted] the fish?"
2: to try, attempt, seek (alt. verbs: "å forsøke" (I, II), "å søke" (III))
"Vi har [prøvd/forsøkt] å fullføre det nye kurset."
"We've [tried/attempted] to finish the new course".
"Jeg skal [prøve/forsøke] å slå rekorden."
"I will [try/attempt] to beat the record."
"Å prøve lykken"
"To try one's luck"
"Å forsøke" only covers the second definition (and would not be preferred in the case of its third example sentence), while "å prøve" actually has two additional definitions not mentioned above. Life isn't fair - even for verbs. ;)
While the two are often interchangeable, "å prøve" has some definitions which are not shared by "å forsøke" (see explanation above).
If the English "to try" can be replaced by "to taste" or "to test", then go with "å prøve".
If it can be replaced by "to attempt", then you're safe to use "å forsøke".
Usually by context.
I'd expect this sentence to have the "want" meaning, partially because we're talking about food, and partially because a native would be likely to opt for "skal" or "har du tenkt til å" for the future meaning to express intent and avoid any confusion.
If you meant "will you" in the sense of someone urging you to or requesting that you try the fish, the above sentence doesn't hold that meaning. We'd find a more courteous way of expressing it.