Contrary to StrongBad, I would say there are important non-terminological differences. While both are junior positions that a recent PhD grad may hold, at my university, a postdoc or Postdoctoral Researcher is intended to be a temporary position for 2-ish years. On the other hand, the Research Associate title is the first in a sequence of permanent full-time research staff positions that goes Research Associate, Research Scientist, and then Senior Research Scientist. While there is no tenure for these positions, the levels are intended to parallel the professor levels here (Assistant, Associate, (full) Professor), and the requirements for promotion are similar (minus teaching).
These permanent positions are expected to continue as long as there is funding to cover them, whereas postdocs are expected to move on after a few years. Given the commitment, most professors, especially the junior ones, will not have Research Associate positions to offer. These are more often affiliated with large labs, centers, or institutes that are large enough and diverse enough to be able to offer long-term funding stability.
There are other differences as well. Postdocs at my university require a special exception to be allowed PI their own grants while Research Associates may PI them from the start without special permission. RAs usually not involved in teaching, where postdoc positions seem to be more flexible in this regard. Also, given the permanence, RAs come with considerably higher status than postdocs, though the respect doesn't really kick in until Research Scientist is reached. Postdocs are a further training position intended to allow a recent grad to finish publishing things from their thesis, branch out into some new areas, and get ready for a faculty position.