Genuine (also called original or OEM) ink cartridges or ink tanks are made by the same company that made your printer (eg Brother, Canon, Epson, HP etc). They are brand new, high quality, usually fairly expensive.
Compatible (also called generic or non-genuine) ink cartridges or ink tanks are also brand new, but made by independent companies, not associated with the printer makers. There are countless generic cartridge manufacturers, mostly in China and quality varies from brand to brand. Good compatibles are almost as good as original ink cartridges, cheap ones can be pretty bad. You get what you pay for...
Compatible ink cartridges are usually cheaper than genuine. This is mainly, because the cartridge manufacturers don't have the same overheads as the large printer makers (Canon, Epson, HP etc), who invest huge amounts of money into development of printer hardware. All the generic cartridge manufacturers design and make is ink cartridges, so they can (and do) market them much cheaper.
Remanufactured ink cartridges are used, genuine cartridges that have been flushed, refilled, tested and repackaged (usually in China). Same as with generic cartridges, the quality varies from brand to brand. Buying "no name" remanufactured cartridges can be a gamble.
InkBank supplies Print-rite compatible ink tanks and remanufactured cartridges when available. They are well made, fit good and the ink is consistently good quality. Not quite as good as genuine cartridges, but considerably cheaper. Should Print-rite cartridges not be available, another brand (eg Ink-tec) are supplied. These are similar quality and work equally well.
Refillable (also referred to as refill friendly) ink tanks are purpose built cartridges - designed to be refilled. They are similar shape as genuine ink tanks, but that's where the similarity ends. All refillable cartridges are transparent (see through) to make it easy to check ink levels and refill. They all come with a fill hole and plug already fitted, so there's no need to drill. But the most significant feature of refillable cartridges is the ink level chip(s). They are designed to be reset - either automatically (when removed from printer), or manually - with a chip resetter, so the printer will accept them as full. Without resettable chips, many printer cartridges or tanks couldn't be refilled at all. Find refill friendly cartridges here.
Note: To comply with printer makers design patents, some recent compatible "chipped" cartridges don't support the ink level display and the "ink gauge" or cartridge LED's may not work. Printer operation is unaffected apart from this.
Ink cartridges at InkBank come with