I am guessing the first one you referred to is Saccharum ravennae. It should not produce any seedlings for you as it is unlikely that the seeds would mature on a plant in your zone.

Maybe the second grass is Miscanthus. Same story as above.

Congratulations on choosing to reuse the organic material, rather than burning!

I am not sure which grass we have so I refer to it as tall pampas grass. What we do with it is just lay it on the ground then cover it with free wood chips compliments of the power company tree trimmers. I only do this in areas where I am not trying to amend the soil, but want a tidy appearance to the landscape. This method provides a very effect weed/vegetation control and I have not seen any grass seedlings from it.