What is the relation between GTK, GTK+ and GTK2?

The first incarnation of the project was called GTK (which stood for GIMP Toolkit).

At some very early point, while the project was still part of The GIMP (and before version 1.0), it was renamed to GTK+. Despite this, people often referred to it as GTK out of convenience or ignorance.

The GTK+ name was used for more than 20 years through versions 1.x, 2.x, and 3.x, but the "GIMP Toolkit" expansion was dropped. I don't know when exactly this happened but perhaps during the 1.x → 2.x transition.

There is nothing officially called GTK2. It's just what some people call the 2.x series of GTK+.

On 2019-02-06, the project was renamed back to GTK, which will affect version 4.0 onwards.

GTK/GTK+ and GTK2 are different versions of the same API. GTK is an old, deprecated version, GTK2 is the previous one, GTK+ 3/GTK3 is the current version.

GTK+ is the correct name of the old API, but most people just call it GTK.

The C++ bindings for GTK+ are part of the project GTKmm.