The MultiMedia cards are the forerunner of the SD card and abandoned by most users.
If you want to see the technical details go here:
The SD type cards were developed a few years later and are now the standard card for most digital cameras.
I would forget the MultiMedia cards as they are not readily available, and offer no advantages over the SD cards.
SD, SDHC, and SDXC offer no difference in image quality.
They indicate the capacity of the memory card.
SD - From about 16gig to 2gig
SDHC (HC means High Capacity) - 4gig to 32gig
SDXC 64gig to 2 Terra Bytes.
What does make a difference is the speed of the memory card.
Any camera that takes HD (High Definition) video, must use a high-speed memory card that is rated as "class 6" or faster.
If you don't, the HD video will look jumpy when you view it because the camera will drop frames when recording the video.
You can read all about the card speed rating here:
Compatible ones are: SD,SDHC,SDXC, MultiMedia cards, MMCplus, HC MMCplus
Are they all the same in terms of image quality? Which one is the best to get?