Memory cards are removable, writable storage usually also based on Flash memory.
(Note: Some devices, like the N91 - or at least it - do not have a removable memory card, but instead a very small magnetic disk drive, a microdrive.)
There are many different kinds of memory cards; different sizes and shapes. Keeping track of all the various different types is a bit of a pain, because there are some many. I try to cover the most relevant that I remember.
Originally Nokia devices used MMC (MultiMedia Card) type cards.
A related card type is the SD (Secure Digital) card. SD cards are physically very much like MMC cards (only slightly thicker and with some extra connectors/leads). However, they can be very different in function (they support additional security features, and can even be used for peripherals; so called, SDIO cards).
One additional thing to mention is that a device capable of handling (reading/writing) SD cards, can also handle MMC cards. The reverse is not true; a device that handles only MMC cards cannot take any SD cards (they shouldn't even fit, because they're thicker).
A "half-size" MMC card is known as RS-MMC (Reduced Size MMC). The first RS-MMC's and devices that supported them operated at a voltage range of approximately 3.3V (Volts). You could call these also high-voltage RS-MMC cards.
Later a version called DV RS-MMC, where DV stands for Dual-Voltage, was introduced. These also got a "marketing name" of MMCmobile for a higher-speed version by the organization that defines the card specifications. The DV cards operate at either approximately 1.8V or 3.3V. With these the key thing to remember is that a device that requires DV RS-MMC cards is not compatible with the "regular"/"original" RS-MMC cards that operate only at 3.3V.
A device that accepts full-size MMC cards will also handle RS-MMC type/size cards. Often RS-MMC are actually sold with an adapter that extent their size to be exactly that of full-size MMC.
(Note: Besides MMCmobile, there are also variations like MMCplus. There can also be MMC ROM memory cards, which cannot be written to.)
Getting back to the SD card type, and speaking of adapters... There is a variation of the SD card known as miniSD. As the name says, it is physically smaller (and available only in smaller capacities). A device that accepts SD cards, also accepts miniSD cards with an adapter that makes it fit a full-size SD card slot/reader.
There's also an even smaller card form-factor known as microSD (it used to be called TransFlash by its inventor company, SanDisk, but as the industry body in charge of SD card related standards/specifications adopted it, it was renamed to microSD to keep the "family name" consistent).
It probably is also worth noting that the SIM (Subscriber Identity Module) is a smartcard with processing power and storage capabity (contacts, messages, SIM application toolkit programs).
(Note: As it is not particularly relevant to Nokia's devices, I'll also ignore Flash memory cards like SmartMedia, Compact Flash or CF, and also the various different kinds of Sony MemoryStick cards; MemoryStick, MemoryStick Duo, MemoryStick PRO, etc.)