To be honest, no, I don't think they're confusing Accept with Upvote. Purely because upvoting is more instinctive an action against an answer than 'Accept' is.
Just think how many other sites there are out there that don't have a concept of accepting answers. Reddit doesn't, forums don't, it's just not as common a concept as upvoting / downvoting.
Not only that, but new users can't even upvote answers (to prevent abuse) so it's not really that clear what they can and can't do to posts. Often people will just leave a comment against an answer saying that it was the thing they were after.
If you want you can leave a comment (not part of your actual answer though) if the asker has commented saying 'you can accept answers if you feel they've solved your problem by checking the 'tick' button on the side', but that doesn't guarantee they'll do so.
Or don't really worry too much. They might come back and accept later, they might never return. But if it's a good answer then you'll get upvotes from other people and your answer will float to the top, showing everyone that it is a good answer.
Plus, just because someone chooses to accept an answer that doesn't mean it was a good answer. Upvotes are a more useful indicator of that.