In my experience, the biggest differences involve incorrect expectations among players about mechanics, setting, and PC behavior
1. Mechanics
The Star Trek Adventures game system is a bit odd. My group adapted to it well enough, but we constantly had expectations about how play would mechanically proceed which were based on experiences with other games. We got used to it but there was a lot of confusion early on. A short tutorial session might be a good idea-- a one-shot adventure that is intended to highlight the core mechanics of the game is something I would have appreciated, as our first couple of sessions ended up being little more than that.
As GM, I strongly recommend practice with the system in advance of play. Nearly every instinct I had as a player was wrong, and guidance from the GM was necessary and helpful.
2. Setting
The other big issue I ran into with STA is that Star Trek not only has a massive amount of lore regarding the setting and detailed elements of how things work but that lore also tended to matter more than in a D&D game.
D&D also has a ton of lore, but it's often poorly continuous across editions, isn't set into very detailed worldbuilding (how do economies work in the Forgotten Realms, exactly?), and can be viewed (by some) as very meta-gamey to be aware of in advance. If your group has even one fan of Star Trek there is a good chance that players will have very clear expectations of how technology works and how specific individuals and groups behave. Those can set up some nice surprises, but can also lead to a lot of frustration.
It is much more difficult to bend the setting of Star Trek into new shapes than D&D. The latter has entire cosmologies that vary from edition to edition. Conversely, that the makeup budget on the original Star Trek series was limited and design of Klingons was later changed has been canonized in-universe as a baroque plot involving genetic engineering and plagues in service of a hazy goal. If you want to make more than very minor changes to the setting, be prepared for arguments. At a minimum, I recommend discussing player expectations for the setting in a session 0.
3. PC Behavior
This one is dependent on players, and is something that our GM for the game addressed early. The game assumes that PCs are officers in Starfleet, which, in D&D terms, tends to restrict allowed alignments. It can be difficult to square being in Starfleet with having non-standard moral aims. Because the setting can be a bit inflexible, discussing this with players early is important. Even if they want to play against type, and you allow it, you as GM will benefit from advance notice and planning.
Miscellaneous
Other things I noticed while playing which were more specific to STA than other games:
- Scenes, characters, and drama aren't so different in STA than in
other TTRPGs. Drama is drama, story is story, and using STA
mechanics rather than D&D mechanics doesn't affect that much. My
only caveat is that Star Trek tends to focus on a lot of big
questions and ideas, and bringing those into games can be very
intriguing. I also find the setting more relatable than magic-filled
fantasy settings, but that may just be personal to me.
- Character background and details are generally more important than in
other games. You get a lot of specific details about major events in
PCs' lives and careers which have direct impacts on their skills and
abilities. The extra detail and integration with character creation
mechanics make it easier to build characters (rather than just
"PCs"), and to fold those details into the game story. Don't miss
this opportunity! I've played other TTRPGs that I liked more, but
never one in which I felt my PC was more well-rounded or more a part
of the in-game universe.
- The rules for supporting characters give an important chance for
variety in play and making sure that ships, outposts, etc. are
appropriately crewed, but also really change the game's distribution
of risks like character death. More disposable crew members are an
important Star Trek tradition, and mortal danger to the main PCs
can (perhaps should) be pretty rare. Make sure to plan content for
both main and supporting PCs, and signpost specific missions as
necessary.
- Spaceships exist in-game as both methods of transit and as
locations for adventures in ways many games don't accommodate well.
Combining those together can be really, really exciting! Trying to
pilot the ship with one PC and simultaneously trying to repair the
engine while fighting off assault teams with the other is a great way
to enhance the drama of a whole encounter and give a Star Trek
experience I (as a fan) really craved.
- So much Star Trek-related media exists that it's easier to find
cool multimedia aids for STA than for some other games. There are
tons of sound effects, video clips, graphics, and so on that are easy
to find and use as mood-setters, visual aids, and props. My GM had an
actor friend record "subspace transmissions" that set up one of our
missions complete with the familiar Star Trek sound effects and
references. It was the most immersive TTRPG experience I've ever had!