I think reach is the amount of people who have seen something mentioning you, so if anyone has shared a link on their timeline it will reach their friends, they've not engaged until they've clicked the link to visit you page. Don't quote me on that though, I only had a few weeks of trying to figure out the insights page before I had to leave.
I've confused myself here. I didn't mean to put Facebook Advertising in the OP, I was talking about general posts of mine. In that situation, is reach the number of people who have been into Facebook that day and seen my post, or the number of their friends that have seen it as the result of a share?
I had assumed 'engagement' was as a result of someone clicking on it or going into my page.
Reach is how many people have seen your post. This includes people who have seen it because they have liked your page and people who have seen it because their friend shared one of your posts. Engagement is people who have clicked on your link, liked the post or shared it.