SQL: Not Like produces different results than what would be Like's opposite

So, I'm practicing for an exam (high school level), and although we have never been thought SQL it is necessarry know a little when handling MS Access.

The task is to select the IDs of areas which names does not correspond with the town's they belong to.

In the solution was the following example:

SELECT name 
FROM area 
WHERE id not in (SELECT areaid 
           FROM area, town, conn 
           WHERE town.id = conn.townid 
           AND area.id = conn.areaid AND 
               area.name like "*"+town.name+"*");

It would be the same with INNER JOINS, just stating that, because Access makes the connection between tables that way.

It works perfectly (well, it was in the solution), but what I don't get is that why do we need the "not in" part and why can't we use just "not like" instead of "like" and make the query in one step.

I rewrote it that way (without the "not in" part) and it gave a totally different result. If I changed "like" with "not like" it wasn't the opposite of that, but just a bunch of mixed data. Why? How does that work? Please, could someone explain?

Edit (after best answer): It was more like a theoretical question on how SQL queries work, and does not needed a concrete solution, but an explanation of the process. (Because of this I feel like the sql tag however belongs here)