Confusing I know!

Google Places is now called Google My Business. Google rebranded in June 2014. HOWEVER here is an important distinction.

GMB is just the name for the business owner interface and the management dashboard. The back end if you will.

The front end, the public facing page is still a Google+ Page (calls it that right in the search results) or many still call it a Google+ Local page, which is still correct, for the public page that we see. The rebranding was just for the business owner interface. (Back end dashboard.)

Does that help clarify?

As stated above simply put they are all pretty much the same thing, at one point they were not but at this point they are the same.

Google places is for business, you can verify local business on google.
If you previously used Google Places for Business or Google+ Pages Dashboard to manage your business information, your account has been automatically upgraded to Google My Business. Google My Business makes it easier than ever to update business information across Google Search, Maps and Google+.