Most vessels carry various 'auxiliary craft' - shuttles, shuttlepods, workbees, etc... to allow crew to accomplish missions.
A vessel must have a specific location on board to contain these craft, whether it is a shuttlebay or specialized docking port.

Docking Port
Many vessels have ports where utility craft can dock other than shuttlebays.
Primary / Main ports are wide portals usually used when docking to starbases.
Secondary / Auxiliary ports are smaller and used when docking with utility craft or other vessels.

Captain's Yacht Port
Primarily used on specific classes with "Captain's Yachts", the port is generally on the underside of the saucer section.
The Yacht port is a modular section and the Yacht may be exchanged for a variety of mission specific components.
See specific ship classes for module types.

The size of a shuttlebay is typically 3x the combined size of the vessels carried.  This allows for workspace around each vessel plus landing / launch space.  Some vessels have "Through-Deck" shuttlebays with bay doors on two sides.  This is to allow continuous landings / launches.
Runabouts / Fighters = size 4
Warp capable shuttles = size 1-3
Sublight shuttlepods = size .05-1
Workpods = size 0.5

In some cases a Captain or crew would prefer to have a Runabout or Fighter rather than the standard compliment of Shuttles/Pods.  This can be done by 'exchanging' shuttles and pods using the sizes listed above.
(1) Runabout / Fighter = (1-4) Warp capable shuttles
(1) Warp Capable Shuttle = (2-6) Workpods
Thus to have a Danube Class you would need to exchange 4-6 Shuttles OR 6-8 Workpods or a combination of both.
Exact ratios depend on the class of shuttle/pod being exchanged.  See pages for small craft for sizes.