Growing Grass In A Forest

I live in a forest type setting and have a lot of trees (tall oak) and with the trees … I have lots of shade.

I have always had a difficult time in getting grass to grow because the trees suck up all of the water and shade out the grass.

I have tried every grass type known to man and ‘even’ when I get growth … it (the grass) dies away pretty quickly.
(no water, lots of shade)

Here is where I need some help …

My back yard, which has the majority of trees and shade has what looks like patches of grass … grass that gets zero water (except rain) and almost zero shade!

The thing is, this grass grows very heartily without any help from me or without sun and shade!?

It looks like there may be two different types and I am posting pictures of both in the hope that someone can confirm that this is in fact grass and what type(s) they are?

Thanks Everyone

The finer bladed one looks like creeping red fescue, which is known for shade tolerance.

I don’t know what the other one is, but I think I’ve got lots of it in my yard. It seems to grow in tufts.

The latter one looks like nutgrass to me. It’s a pernicious weed here.