Tiffany, I also love that one in your last photo! It looks familiar, reminds me of Bamboo Palm, Chamaedorea seifrizii but I get palms confused all the time, especially those in the Chamaedorea genus; they all seem to look alike to me. If you ever find the ID on that beauty, please let us know!
A very knowledgeable horticulturist (I think it was
@Metrosideros) once told me the differences between the Cat and Parlor Palms but I lost my notes when my computer crashed awhile ago. I think one has more of a clumping and suckering habit than the other.
I have a few potted palms that stay outside year-round; they never seem to do well indoors. I moved this small one inside a month ago but I'm sure I'll be putting it back outside soon because I know it will get ratty looking if it stays inside for long. It was labeled as "Parlor Palm" and I'm sure it's a Chamaedorea but not sure if it's C. elegans or C. cataractarum:
I have one Lady Palm (Rhapis excelsa) that I purchased seven or eight years ago. I almost lost it to a winter freeze a couple of years back but it seems to be recuperating and growing. We just moved two months ago and we have Lady Palms spreading by their rhizomes in a couple of areas of the yard. I found some sprouting up in the screened pool area so I dug them up and potted them but they've not done too well ... possibly because of the horrendous heat as well as lack of sufficient rain and possibly from too much sun due to my short attention span.
In-ground along one side of the house, the one that I almost lost to a freeze (with Caladiums, etc.) and one I potted up that's looking so hot; one stem is bare:
Pigmy Date Palm (Phoenix robellini) and I think both of these are Cat Palms (Chamaedorea cataractarum):