A boost is like a Twitter "retweet", it reposts the content to the booster's personal timeline for people who follow them to see. For example, right now, two people have boosted your question. If you go to "more --> activity" you can see who boosted you, go to their profiles and find your comment "What's the difference between a favorite and a boost?" on their respective profiles under boosts.
Upvotes are actually your favourites - https://kbin.social/fav
It's a bodge from when kbin and Lemmy started federating with each other and had to merge their systems. Before that boosts were the kbin upvotes, but they aren't used on Lemmy.
Another important difference is the "reputation score" for each user profile.
Favourites (up arrow) on posts and comments do not contribute in any way to reputation.
Reduce (down arrow) does reduce your reputation by 1 point
Boost (bottom of comments) increases your reputation by 1 point.
I understand the reasoning why the devs separated favourites and boosts but your average user (especially reddit refugees) do not understand this. I think that reputation should also include favourites in the calculation.
I personally use reputation as an indicator that I'm contrbuting in a postive way to a community not really as a winning "fake internet points" thing.
That is most likely unintentional though. Boosts are like retweets, they get posted for your followers and are publicly visible. The reputation system of old was based on either boosting - the post is good so you want to show it to more users - and reducing, hiding and burrowing it. So it wasn't like reddit, it was twitter with downvotes.
I'm fairly sure it will get changed eventually. How exactly, I'm not sure - lemmy doesn't have any reputation at all so it might even get removed entirely.