in order of magnitude:

worldship/worldstation: massive government vessels bristling with defensive armaments, but they are only intended for civilian use. churned out of top-secret factories at a rate of a few per century, these vessels are meant to simulate life on a specially designed, sculpted planet. their interior consists of slowly turning plates of planet material interspersed with glass panels to allow in sunlight and starlight, with entire ecosystems contained within. they range wildly from the size of a moon to the size of a small gas giant. http://img07.deviantart.net/08e2/i/2008/113/e/a/l3_colony_by_samurairyu.jpg looks kinda' like this, except, y'know, with vigil architecture.

ark: ships of very large size designed to comfortably accommodate immense numbers of people. not quite the size of planets, but they are meticulously designed to accommodate a comparable population. these vessels are usually made by the government to help facilitate things like evacuations or the transportation of large populations from dying worlds.

flagship/capital ship: a ship of primarily symbolic power, usually carrying advanced and experimental weaponry and wielding unrivaled size. these military ships range in size from tens of miles in length to the size of a small moon. although they wield great power in combat, the flagships are mostly intended for a sort of symbolic power; they are marvels of engineering achieved through unity and organic/AI cooperation, and represent the might of whatever faction they belong to. the vigil's flagship is the Void Maw; the ICA's flagship is the Forbidden Sky; the VSIE's flagship is the Titan Hunter.

dreadnought: referred to by a lot of dangerous names, despite the flagship's reputation the dreadnoughts are some of the most widely feared battleships in the universe. wielded by many forces, not just the vigil, dreadnoughts are massive ships that can be miles in length and wield immense quantities of weaponry. they are the spearhead of large assaults, the first wave of a surely devastating attack, the most mighty and deadly ships besides the flagships. these vessels carry crews in the hundreds and are lined with all manners of weaponry and are usually carriers for many other ships as well. dreadnoughts are the fever pitch of a battle, and a sign that things are getting serious, and it is extremely rare that a dreadnought is completely destroyed in battle.

'heavy' warships: a sort of catch-all for a number of specialized battleships in between the massive dreadnoughts and modestly sized frigates. these warships are very common and tend to spearhead smaller attacks, ranging fairly wildly in size; a ship of this type above a mile in length is instead usually called a dreadnought.

frigate: sort of the 'medium' vessel, these are usually well armored and well armed. they are the staple of almost any fleet, on offense or defense, and tend to be more than a thousand feet in length. they sometimes carry dropships or fighters that can deploy and help back up the frigate when overwhelmed or when bringing troops to the field.

cruiser: a fast, light ship. these vessels carry either a skeleton crew or no crew at all, and although they are not particularly well armored, they can still stand up to some damage and have devastating weaponry. these vessels are some of the most common in wartime, especially for attacking fleets, as they can overwhelm larger vessels.

freighter: civilian ships, which vary wildly in size and can sometimes even rival dreadnoughts in size. they are pretty much exclusively used for carrying massive quantities of cargo. similar ships but for passengers are often called cruise vessels or arks (although this is more correctly used to refer to the above ark ships).

dropship/carrier: carrier ships are some of the most common in the universe. they are small, multi-purpose ships. in military contexts where they are used to deliver soldiers to the field, they are referred to as dropships. carriers can be the size of buildings or slightly more, and such vehicles are often lived in by nomadic civilians or used for carrying fairly large amounts of cargo, but vehicles ranging from the size of cars to airplanes are commonly referred to by these names as well and are used for quickly deploying soldiers or the unmanned movement of cargo.

fighter/chaser/skipper: these vessels are known by different names depending on the context they're used in. in military contexts, fighters are small, almost always unmanned, heavily armed but lightly armored vessels about the size of a car or semi-truck that are extremely fast and maneuverable. they are often intended to slam themselves into enemy ships when critically damaged, and are considered expendable, cheap swarming vessels that are meant to overwhelm. in law enforcement context, chasers are similarly sized unmanned vehicles meant to chase down fleeing vessels or vehicles, or to hunt targets. in civilian use, skippers are small, cheap vehicles meant for the use of one to four individuals for personal space travel, and are the most common ships in civilian use.