Look at www.microsoft.com\sharepoint
<http://www.microsoft.com/sharepoint> the web site should help you
understand the differences. sharepoint Portal Server provides search,
basic document management, and a portal engine. With this you can set up
areas called workspaces for a group of users. Some of the things that
a portal user can do is search many different types of content sources
(file shares, sharepoint servers, public folders in exchange ect) from
a single portal page. Administrators can also create or add new parts
to the portal, say a web part that integrates with your time keeping
system. You can check in/out and even version documents as well as do
some basic workflow.
Sharepoint team services are a separate product that comes with Office.
I do not work with STS that much but I think it is safe to say that it
is a team collaboration piece. You can create a team site add various
lists to it such as contacts and store some documents. It really seems
to work well with teams working on a project - single place to go for
all your project needs.
Others can jump in and add more to the Team services piece.