The only differences so far are the seeds you start with (though all races seem to start with wheat), race specific armor/weapon/food recipes you start with, and like you said, cosmetics including your spaceship and randomized names during character creation.
Chucklefish didn't want one race to be able to do something that another couldn't. All race specific recipes can be found by other races later in the game so everyone will eventually have access to all the same things.
The maybe not-so-noticeable cosmetic changes would be what one race has to say about another races technology, using the magnifying class on the right of the screen. For example, my Hylotl commented on the torture devices and large green cloning(?) tanks in the Apex outposts very negatively saying such things do not belong in civilized societies.
Your race will not affect how other races act towards you. If you stumble across any villages, they will pay you no mind (as long as you don't have a weapon equipped) and merchants will sell to you. If you come across a dungeon, you will be attacked on sight. Even if you are the same race as the dungeon.
Update for Upbeat Giraffe released 1-29-15:
A new class has been added, the nova kid! The most interesting part about this class is their starting weapons include ranged weapons unlike the other classes that only get melee weapons.
Other than the nova kids, anything class-specific still seems to be cosmetics (starting armor, craftable weapons, recipes, etc.), most notably added in this update your ship's AI (S.A.I.L.). Also added in this update was the ability to upgrade your starting ship. These upgrades add sections to your ship giving you much more space to decorate, set-up a farm, or really anything you would want to do on your own gigantic spacecraft. Each classes ship has it's own unique style.