Yes, you're right, it does effectively make the variable public. But there's one important difference, which is that it gives you the ability to change things later on: you can remove the setter if you want, or make it private, without affecting code that reads from the field using the getter.
If you'd just made the variable public, you wouldn't be able to stop writes to the field without also breaking reads from the field.
It has other advantages. You can make the access synchronized if you want to later on, without breaking client code, for instance. In short, it allows lots of modifications later on that wouldn't otherwise be possible without causing lots of breakages in code that uses the class.
And you can add extra logic that logs whenever someone writes to the field, or prevents certain threads from writing, or whatever... you can change the type of a field from a HashMap to a TreeMap if your getter abstracts it away and just returns a Map... etc.
