The Federation Faction is one of the 3 starter factions you get to pick in Pixel Starships. The other two being the Pirate and the Qtarian. The Federation is usually in the middle in terms of grid amounts.
The differences between the other 2, is that the Federation ships have a much more rectangular design. This makes it very effective for maximizing space and sandwiching. This is usually the most recommended ship for beginners.
The main color scheme for the Federation ships is a light blue and grey. It also has an eagle insignia which is probably the Federation logo. It also has a different branch of ships which can be switched to at level 10.