What type of D chord is this:

|-7-
|-7-
|-7-
|-5-


And what type of C chord is this:

|-5-
|-5-
|-5-
|-3-

I'm doing Aerosmith's Seasons of Wither as my beginning full song, and it's surprisingly easy. I find these chords very challenging though, for I have small fingers and hands. I'm gonna work to get it though, and I would love learning the exact names of those chords.

Thanks