On Tython I've encountered two trainers, and the second didn't have any new moves to offer me. Do all trainers teach the same moves? Or do I need to seek them all out at the right levels in order to learn everything?
Are all trainers the same
star-wars-the-old-republic
Related Solutions
Crew Trainers can be found both with your faction's fleet and on your faction's capitol city, and possibly on other planets as well.
You can have three professions at a time, but only one of them can be a crafting profession.
Each crafting profession has recommended gathering professions for it. For example, Artificing (to create light saber mods) recommends Archaeology (for crystals) and Treasure Hunting (for gemstones).
Bonus tip: Talk to every trainer before choosing your professions to complete your codex entries for professions.
For the most part, your crew will do the crafting and gathering for you.
Once you have multiple crew mates, it's a good idea to send the ones not with you on crafting or gathering tasks.
When you visit a crafting trainer, by default you only see the items you can craft with your current crafting skill. So, new items will appear there when your crafting skill reaches higher level.
But you can let it show all schematics (including those that you can't craft yet) by choosing "All" instead of "Trainable" in the dropdown in the upper right corner of the window. This way, you can find out what level of the crafting ability do you need to craft the better items.
In the screenshot above, you can see that I have chosen "All", so that even schematics that I can't craft yet (that require level ≥ 380) are visible.
Best Answer
All the trainers (that are appropriate for your class) will teach you the same skills. In the top right (if I remember correctly) of the training menu you can choose to display the skills you haven't learned yet or don't have the level requirements to learn yet.
All the trainers teach you the same basic skills. IE. All Sith Inquisitor trainers will be able to teach you force lightning at level 2. Multiple trainers are scattered out to make it easier to get your skills when you level up.