If you "encounter" something or someone, it is usually not expected and more of a surprise, For example, "I encountered aliens" or "The enemy fleet encountered their rivals on the sea.: If you were to "find" something or someone you would be actively looking for that thing or person. For example, "I found the lost pirate's treasure" or "I found my cat hiding in the attic." "Encounter" implies chance while "find" implies intent.

"To encounter" and "to find" are very similar. One difference is that "to encounter" has the connotation that the "encountered" situation is unexpected. It is also more often used with people, situations, and events than objects. For example, if you lose your house keys and look for them, you would "find" them, not "encounter" them. If you are going to see your friends, you would "meet" them, not "encounter", but if you unexpectedly see them, you can say you "encountered" them. You could also use "found" or even "unexpectedly found" in this situation. "Encounter" can sound a bit awkward and old-fashioned in most situations and "find" is much more commonly used. Actually, the situation where "to encounter" is most commonly used in everyday conversation is when talking about paranormal events, like in the phrase "alien encounters".