what is the difference between a dc motor and a dc motor with gearbox?

It just mans the motor is supplied with a gearbox already attached, rather than you having to get a separate one if you need to reduce the output speed.

Because such assemblies are so common, they are generically known as "Gearmotors".

It also means you have to chose or specify the gearbox ratio and style in addition to the motor specification.

It could be worm, spur, epicyclic, harmonic, bevel..
For high-precision use, some types also come in different grades with different backlash specifications.

Examples:
https://www.pololu.com/category/51/pololu-metal-gearmotors

http://www.grainger.com/category/gearmotors/power-transmission/ecatalog/N-aql

http://www.baldor.com/brands/baldor-reliance/products/motors/gearmotors/dc-gearmotors

The one with the gear box almost certainly has slower speed and greater torque.