In the second image it looks like fern, so it's not unlikely you have Bryopsis in your tank. It would be easier to identify if you manage to get a little bit out with tweezers or so and then put it into a small container with some tank water so it can "unfold".
In case we can positively ID it as Bryopsis, you could try to follow Julian Sprung's suggestions in his booklet "Algae - A Problem Solver Guide". Bryopsis "[...] proliferate when there is some ammonia and or nitrite available. Strong biological filtration (nitrification and denitrification) limits its growth" (chapter 3, page 47). Additionally herbivores and manual removal are suggested.
If your tank is young and goes through the ugly phase it's possible that it will solve itself, but I can't promise that as I have not had the chance to observe a Bryopsis ugly phase yet. From what I've been reading here on R2R over the years many people give up sooner or later and use Fluconazole, but I would wait for others to chime in before using the chemical option.