Are those lizards Anoles? I here they are a big problem down there.
Yes, they are both Anoles, but the first one is a Carolina anole (other names:
American green anole,
American anole, and
red-throated anole.) and is native to this area; they are a bright green color, but can change to a brown color.
The second one is a Brown anole and is an introduced species from Cuba and the Bahamas. They are brown in color and cannot change color; however, they come with various markings, so they are not just a simple brown color, some of the markings are very interesting looking.
There are some that say that the introduced anole is displacing the native anole, so maybe that's the "problem" you're thinking of?/. I think there's something to this, but it's not critical in my observations, I have both species and there seems not to be much of a problem. There is also some information out there that indicates that the Green anole is showing signs of fast-paced evolution, making them better tree climbers.
I have seen them way up on my live oak tree and the only way they could have gotten there was from the base of the tree (which is a very large tree). The other day I was blowing leaves off my roof and shook a branch to knock more leaves down and a green anole fell to the roof; I picked him up and put him back in the tree, he was fine.
Here's more on that:
http://scitechdaily.com/rapid-fire-evolution-green-anoles/