Some fountain pen manufacturers make ink cartridges that will only fit their pens. Therefore, you will need to ensure that you are buying the right ink cartridge for your pen.
Parker, Lamy, Cross and Sheaffer pens most notably will only accept their own ink cartridges.
The majority of other pen manufactures will accept the international standard ink cartridges. Therefore, these can be interchangeable.
International standard cartridges are available from Pelikan, Waterman, J. Herbin and Diamine.