Yes. No wrasses for you.
To me the ones on the glass look like hydroids. People get confused because there are a few types, colonial hydroids are much more of a threat because they cluster and sting in a particular spot, but these aren't those. These are just hydroids, the regular new tank kind. They have a jellyfish-type of lifecycle pictured here
They look very much like aiptasia, and alight on a surface to filter feed, then send out little snowflakes in the water. I think a lot of fish eat them since they are almost never a problem (as opposed to the other colonial type that post up on a spot and start claiming territory).
I, like many others, had a bloom in my tank until I added a fish. Then I never saw anymore little snowflakes on the glass or aiptasia-ish things on the rocks for over a year. A month or so ago I moved some rock into the sump to clean it up away from the light for my tank upgrade ... immediately covered in hydroids. And now I see the occasional snowflake doing the weird jelly swim in my DT.
My first fish was a chalk bass, hardly known for pod predation but he cleared out the DT of hydroids anyway, or else some kinda bigger worm took hold like a peanut or spaghetti. The melanurus probs helped too, I got him about 6 months in. If you're trying to culture micro food for a mandarin, you will see your tank blow up with stuff like this. It's good to be cautious about which things you allow to proliferate. These hydroids are not the critters you need to worry about though. The flatworms might be a diff story. I'd not let that get out of hand.
EDIT: here's a pic of the ones in my sump. It was aiptasia-ish enough to scare me so I posted a thread on it. It didn't occur to me that I might still have hydroids around since I hadn't seen them for over a year. But the consensus was that I do, they were just hiding and waiting for the opportunity. It's kinda remarkable how resilient these critters can be, especially hitchikers. Respeto!