Seems like all this certificate does is make communications secure between
my users and the server.
Actually, it's the HTTPS itself that makes it secure. All the certificate does it tell visitors to your secure site that you managed to convince Verisign or Thawte that you really are the person or entity you claim to be, and that you legitimately own the rights to the domain name that you wish to certify. And perhaps a few other things, too, but it's not very extensive in terms of what they do.
The merchant account and credit card processing would be an entirely
different thing right?
Indeed. Let me second Jason's recommendation of signio (now part of
verisign)--though in the recent project I worked on using signio, we
used the entry-level version of their processing that was entirely web-
based: you link to a secure page of theirs for the actual card entry, and then they link back to you if the charge goes through. Completely adequate for small and medium transaction volumes, and the price is right.