I'm not aware of a difference between these two labels/positions. As far as I know they are two labels to identify those who believe that God is the creator, evolution was the process, and God was continually guiding and even enabling the process (since it's pretty far-fetched to think that evolution could possibly have happened without divine intervention).

The term I prefer to use is "evolutionary creationism," because "Creationism" is the main noun and "evolution" is an adjective. It puts the emphasis on creation, with evolution as the modifier. As you can see, "Theistic Evolution" seems to put evolution in the main position and theism as the modifier, and "creation evolution" is difficult to understand, in my opinion. That's why I prefer "evolutionary creationism."

Is there a difference between these 2 terms or belief sets? I ask because I generally think evolution had a part in God’s plan, but I’m not convinced of all evolutionary claims (IE – we started as 1 single cell/organism and become this complex). Do these make different claims of evolution? I’ve had discussions with YEC peeps and they seem to think I believe in all the scientific 'claims' and muddies the discussion. I say claims loosely because they see evolution as a buzz word and get some information from media outlets to try to assert what all of science believes. Can be trying at times...

Curious if claiming a different name for my stance helps at all or if there is a way to properly present what evolutionary claims are proven and believable within the biblical space vs those that are not.