No, the two are completely different.
Grid hosting involves having a cluster of servers all able to serve up the pages for a single website. The load between the servers is load balanced.
As Mikka references, DreamHost PS uses Linux VServer, which is a server virtualization technology. This is all about accounts being tied to a “dedicated” virtual server. So you get what amounts to a server-within-a-server all to yourself.
Here are Wikipedia articles on the two technologies:
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