Space Station

A Space station is a stationary, artificial structure in space usually designed to support a crew at a specific location. They serve as support stations for starships, observation posts and defensive installations.

Space station is used as a general term for any stationery space facility, but there are a number of related, more precise terms;

A Starbase is sometimes used to refer to a large Federation support facility, sometimes planet-side but usually orbital. Spacedock is a term used exclusively (i.e. Starbase 1, Starbase 82, Starbase 157, Starbase 621).
Deep Space stations are a designation used for Federation stations on the fringes of Federation space. They have similarities to the role of Starbase but the term is rarely used interchangeably (i.e. Deep Space 9, Deep Space K-7, Deep Space K-13).
Research or science stations are purely scientific outposts (i.e. Delta Volanis Science Station, Kyana Research Station)
Trading stations are commercially operated stations (i.e. Treasure Trading Station)
Outposts are small border installations for observation and defense (i.e. Sierra Outpost II).
Spacedock is rarely used, and relates to it being a major docking point for orbital starships (i.e. Earth Spacedock, Vulcan Space Dock).
Shipyards are a stationery facility dedicated to the design and production of starships. They are often a large collection of small stations and dry docks (i.e. San Francisco Fleet Yards, Utopia Planitia Shipyards).
Listening posts are communication relays, sometimes unmanned and sometimes covert, that are used for surveillance transmissions (i.e. Lackey Listening Post, Bomari Listening Post).

All Deep Space Stations are Starbases.

Not all Starbases are Deep Space Stations.

A Deep Space Station is simply a Starbase on the fringes of UFP territory.

Deep Space 3 was the last port Geordi La Forge's mother was at before her and her ship the USS Hera went missing.

Deep Space 4 was the only place with records on Annika Hansen's (7 of 9's) family. It was also the destination of Professor Richard Galen when he was unlocking an ancient DNA code (in the TNG episode "The Chase.") From this appearance we know that DS4 is on the Beta Quadrant side of the Federation.

Deep Space 5 sounded the alarm for the Borg invasion in 2373 that culminated in the Battle of Sector 001 (the events of Star Trek: First Contact).

And of course, Deep Space 9 sits in the Bajoran system, on the border between Cardassian and Federation space, near the Demilitarized Zone.

From what little information we have, I assume that the Deep Space stations are the last friendly ports on the frontiers of Federation space. Starbases seem to be a more regular feature spread throughout Federation territory.

Starbases are the primary facility of a star system. They can be on planets or on stations. They are the base of the star.

Space Stations are simply stationary objects that may be independent, attached to a starbase, or attached to a planetary government.

Deep Space Nine is technically a Starbase, based on a space station.

Star Bases are UFoP owned/operated within their boarders.

Deep Space Stations are basically outposts/forward operating bases run by UFoP but may not be within UFoP boarders

I'd think that Deep space stations, are the more important stations, where a station is set up at an important site, say they converted Terok'Nor to Deep Space Nine because it was at the wormhole or simply because plot reasons. Or maybe because it's on the cardassian border.

(I don't think they knew of it at the time, my DS9 is a bit fuzzy)

There isn't much information about what a Deep Space station is other than it's name, and their purpose Deep Space 4 could be in the Beta Quadrant because They needed a more purposeful starbase closer to the Romulans and Klingons.

But another theory could be Deep Space stations have an intended objective. While Starbases are placed all around Federation space for Cargo holding, Trading, Housing, And ship repairs/stuff like that. I'd assume there are only Nine Deep Space stations because well the most recent one being DS9 there'd be no point to randomize numbers. SO each station having a specific purpose, DS9 being keep the Cardassians away from the Bajorans and out of Federation Space/Protect the Wormhole; and Deep Space 4 could be Keeping the Romulans and Klingons on their side of the Galaxy(beta quadrant) or some other purpose.

EDIT: Another theory could be that the Deep Space stations are just on the edges of Federation space/outside of it, out from any immediate assistance, Which is why there are so few.

TL;DR Starbases are basically future gas stations slapped into a walmart and Deep Space stations are like FOB's or just a station with a specific objective rather than be a stopping station.

One thing I've noticed is that starbases are not always space stations. Many of them are planetside facilities. So one difference is: deep space stations are space stations and starbases aren't necessarily.

I think it's mostly to do with whether they're in Federation space or not. K-7 was strategically located near Sherman's Planet, which the Federation and Klingons were competing to develop, while DS9 was in Bajoran space.

I am not sure if I am correct, but I had always thought that there were three main differences, between Starbases and Deep Space Stations.

Starbases were built by Starfleet. A DSS, on the other hand, was a structure which was found or salvaged by Starfleet, which was originally built by someone else, and then adapted for Starfleet use.

Starbases were located closer to, or in direct orbit of planets. DSS could be just that, in deep space. DS9 was not originally in the orbit of Bajor.

Starbases were owned exclusively by Starfleet, free and clear. A DSS might be at least partly owned by someone else, and would be jointly administered by Starfleet, along with its' original owner.

Not all starbases are space stations.

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