Ships and stations lack artificial gravity (even the affini ones) so low spin gravity (part of the ship spins) and linear acceleration (where acceleration simulates gravity) are both in use.
Affini ships are massive, the smallest support vessels of the compact rivaling the size of the biggest ships the Accord ever had. Command ships are the size of countries. Stations and mega structures get even bigger! The affini have brought a few of their world ships into terran space, but those deep in Compact space get stupendously large.
The jump gate structure around Sagittarius A*(the black hole at the center of the milkyway) is bigger than the sun by multitudes! It connects to various other galaxies the Affini Compact has domesticated.
Affini jump drives are faster, longer ranged, more efficient, faster to charge, and ‘quieter’ than Terran jump drives by orders of magnitude. But it can still take weeks to get across the milkyway! Their ships do have limits on exotic matter, and power.
Affini ships mostly have very planty names just like the affini themselves, but have a wider variety of naming conventions, though they often take a name pronounceable by the native sophonts of the given space. Which in terran space is often planty.
Terran ships are small cluttered and have a very hard sci-fi look. Ones for quadrillionaires might have that sleek chrome finish, but most are just clunky and industrial looking. Terran jump drives are—on a galactic scale—very short range. They range from small escape pods up to a mile long dreadnaught.
Pirate ships exist! Most famously the Leaena Dei was captained by the infamous Felicity Irrien, managed to cause the Great Recession of 2548!
The Accord used ships for all kinds of things but mostly for corporate or military interests because no one else could afford spaceships in a fascist capitalist empire. Of course that meant most accommodations on terran ships were cramped. Also many got stuck eating Synthecubes, or another form of rations for cost reasons.
For getting off high gravity planets, launch loops were common, along with mass drivers, and classic rocket launches.
Most terran navy ships have the prefix C.N.S. (cosmic navy ship) or sometimes T.C.N. (Terran Cosmic Navy), often terran's drop any prefix and just say the ships name in conversation. Major corporations typically use their own branded company prefix.