Aloe vera for the second one, first one - not sure. Wonder Lzrddr will check this...

The baby come from the big plant. So, usually that means they are the "same kind"?

You've got the same Aloe vera chinensis that's commonly sold as Aloe vera (which has yellow flowers and its rosette is more compact). A. v. c. has orange flowers as is a flopper if not grown in direct light (like mine isn't) - it tightens up in more sun / less water but you want to acclimate it to full sun.