This brings up an interesting (to me) question. Never, in the original series and first six movies did they ever use the Away Team term. That was invented for TNG and picked up for Kirk's Enterprise crew when the films were re-imagined by J.J. Abrams (along with Warbirds). The original conception, if I remember correctly, for the Away Team was a team of crew members specifically assigned to do missions "away" from the ship, leaving the captain and other important staff members out of harm's way. This is in direct response to criticism of Kirk and his senior staff constantly beaming in to dangerous situations. So, Riker would head up his Away Team, which wound up being other stars of the series - practically anyone except Patrick Stewart (until he bitched about it).
A Landing Party - as seen in the Original Series - was pretty much any group of people beaming down. The Away Team felt like it was supposed to be the same specific people assigned to do planet duties: the Exec, the security chief, the guy with the VISOR and the science officer. Plus whatever specialists they needed to "join the away team." Like it was "The Away Team." This is why it still kinda rankles me that Kirk's era films started using the term. Kirk didn't have a set team. He would beam down and the people joining him would be who was needed by the writers to be in the episode. They seemed to be two different things.
Maybe this should be its own thread, or maybe it's just me.