Starships

Starships are, as the name suggests, spaceships capable of traversing to other stars. The basic rule is simple: If it uses a Hyperdrive, it's a Starship. If it solely runs within a single star system instead, it's a Spaceship. An important aspect is that most Starships are designed to never even get close to a planet, depending on space stations and spaceship transports to interact with planets.
Due to their large size, most Starship classes are only built at a few different shipyards. The most famous one are the Luna Shipyards, located at Sol System. These are the only shipyards that can mass-produce Titans, the largest ships capable of entering Hyperspace. Luna does not produce military vessels, so companies use their own shipyards to retrofit Titans into Leviathan warships.

Smallest Class

Hopper

Largest Class

Titan/Leviathan

Highest Known Relativity

3.9

Functionality

Without going into boring details, there are two units of measurement that matter when venturing into Hypersea: Relativity and Tranquility. Relativity is basically how much resistance a ship needs to overcome, while tranquility is how much turbulence a ship may face.
Large ships have a lower maximum relativity, which means they can only access shallower parts of Hyperspace. Meanwhile, there's a minimum as well: Too small a ship, and the Hyperdrive fails to properly control the ship. Another thing to remember is that thrust is constantly required. As such, a ship will fall out of Hyperspace if it runs out of fuel or its drives fail.

Production

Because most Starships are massive and aren't built to handle atmosphere, they need to be produced at low or zero gravity. This means a shipyard needs a proper building spot in space, but also a supply chain of crew and materials to provide it. There are few systems that can reliably offer that without being constantly attacked by pirates or rival companies.
As a result, most shipyards are in long-established systems which are already significantly terraformed. The remaining ones are built in asteroid belts rich on iron. And all of them are heavily secured, since a shipyard is usually worth more than the rest of its system.

Classes

There are plenty of ship classes, including overlapping definitions. The following four classes are most relevant and universally recognised.
Hopper: The smallest sizes that can actually still enter Hyperspace. They can only do quick hops before running out of fuel, so are used to travel between neighbouring systems or a Starship and mining sites.
Titan / Leviathan: The largest class, which can only traverse the Via Solaris. Transporting trade goods, armies, and Terraforming Seeds. Leviathans are warships made to defend or conquer entire systems.
Wolf: The Wolf class consists of long Spaceships that are used by rich pirates and other warmongers. Designed to house large amounts of weapons and cargo, these ships also can handle low Tranquility and high Relativity. This lets them easily and stealthily approach other ships, then escape any chasing patrols.
Raven: The Raven class is smaller than the Wolf class but of similar design, and are primarily used as scouts by poorer Pirates. They cannot house many weapons, so they find prey for Wolves, then scavenge the remains. They do so in the hope of striking it rich with a lucky find.

Purposes

Even ships starting equal will end up significantly different in the end, depending on what they were built for. Even Titan vessels have varied purposes: Mass transport of cargo, population, terraforming materials, or an army ready to take over a rival planet.
Some small ships are solely focused on transporting people, so comfort and quick trips are what it's all about. Cargo ships tend to get some weapons and better sensors for self-defense against pirates, while comfort and internal safety are irrelevant.
Scouts are all about the sensors, as well as being able to travel fast through highly-turbulent areas of space. These ships are lightly manned, but often have strong Hyperdrives so that they can hide in high-Relativity areas. They also are equipped with anti-sensor defenses.
Defensive warships must be large enough to support both high-quality sensors and a massive arsenal. Offensive ones may be stealthy and fast, as well as be equipped with boarding equipment.
Lastly, mining carriers are ships that can transport both large amounts of cargo and multiple Hoppers, which let them mine more at the same time.