No, Google My Business is not the same as Google Business Profile. They are very similar, but there is one thing that clearly separates the two: the businesses that will have access to them going forward.
Bigger businesses with multiple locations will keep enjoying the Google My Business experience. The only difference is the name change from Google My Business to Business Profile Manager. On the other hand, smaller businesses with only one location have been transitioned to Google Business Profile, which largely is the same as Google My Business, with some slight new changes added in the process of claiming and editing business listings.
Note: Don't worry! If you already listed your business on Google My Business, you won't be required to make any changes.