VCR = Video Cassette Recorder. For consumers this generally means 1/2" VHS, but other VCR types include Beta, S-VHS, VHS-C, 8mm, Hi-8, Mini-DV, 3/4" U-Matic, Betacam, M-II, etc. The cassette eliminates the need for handling, threading and thus damaging the fragile Saran Wrap-like tape inside. When the cassette is loaded, the mechanism opens the cassette flap and pulls out the tape and threads it around the various guides, heads, spinning video head drum, etc.
VHS = Vertical Helical Scan originally, later changed to the more friendly sounding Video Home System. Developed by JVC for consumer use. The #1 home video tape format today.
VHF = Very High Frequency. TV channels 2 through 13. (Sometimes confused with VHS.)
Beta = Named after a Japanese word for "the whole thing" because it recorded video on tape without guard bands, to eliminate wasted area. Developed by Sony, it lost the Beta vs. VHS home format war.
Betacam = The successful version of Beta, using a Beta type cassette but with better tape and running through several times as fast. Later versions include Beta SP, Digibeta, etc.
VHS-C = Compact VHS cassette for portable use, holds 20 minutes of tape. Being made obsolete by Mini-DV. Its sole advantage is that the tapes, with an adapter, will play in your VHS machine.
S-VHS = Super VHS, which has 60% better sharpness and will not play on an ordinary VHS machine. Some newer VHS machines with "quasi-S" can play but not record S-VHS tapes.
SVHS ET = Super VHS Expansion Technology, which has near S-VHS definition but is recorded on regular VHS EHG tape. About 60% better sharpness and will not play on an ordinary VHS machine.
8mm and Hi-8 = Uses exotic 8mm (5/16") wide tape in a small cassette, for portable camcorders. 8mm is better than VHS, and Hi-8 is better than S-VHS. Will likely be  made obsolete by Mini-DV.
Mini-DV = Digital Video tape, 1/4" wide. Used in the best quality consumer camcorders. The quality rivals professional Betacam equipment costing 10 to 100 times as much. For serious work, it can be copied to a computer for editing, and then to another DV tape with no quality loss.
Digital8 = The same recording quality as Mini-DV but using an 8mm wide tape. Not interchangeable with DV.
DVD = Originally stood for Digital Video Disc, someone decided it should stand for Digital Versatile Disc. DVD-R and DVD+R are the Recordable versions, which will play on most DVD players, allowing your personal films and tapes to be preserved, and not just blockbuster movies.
VCD = Video Compact Disc. This is a low-cost system of making video discs, recording on regular audio or computer type blank CDs. Developed in China, it records up to 80 minutes of highly compressed digital audio and video of about VHS quality. It will play on many modern DVD players.

NTSC = National Television Systems Committee. Came up with the USA system of color TV. Frequent problems with color constancy has led to the nickname "Never Twice the Same Color."
PAL = Phase Alternating Line. The main European system of color TV. Unlike NTSC where technical problems give purple or green faces, PAL color gets washed out instead. An improvement?? Sometimes nicknamed "Problems Are Lurking." PAL-M is a hybrid used only in Brazil, combining NTSC-like scanning with a variation on PAL color. PAL-N, used elsewhere in South America, records and plays normal PAL tapes, however the VCRs put out different color signals to the TV set, to suit the local broadcasting system.
SECAM = Sequential Color Avec (With) Memory. Promoted by France, which evidently wanted a more complex and expensive system than either NTSC or PAL. Sometimes nicknamed "Something Essentially Contrary to the American Method."

Hi-Fi = High Fidelity. A sound recording method used in 8mm, Hi-8, VHS Hi-Fi and S-VHS machines where the audio becomes an FM signal (something like an FM radio broadcast) that is recorded and played with extra heads on the spinning video head drum. This yields excellent sound fidelity, with low noise and other defects. In VHS and S-VHS, a conventional linear low-fidelity track  (somewhat akin to AM radio) is also recorded, for playback on ordinary VCRs.

SP = Standard Play speed on VHS tapes. Should normally be used for the best quality and reliability, and ability to be played on various VCRs. (In Betacam and 3/4" professional tape formats, SP means instead "Superior Performance" and the speed does not change.)

EP, LP, SLP = Extended Play, Long Play, Super Long Play. Slower tape running speeds used when greater economy from longer playing time outweighs the desire for maximum quality. The narrower video track results in higher video noise, more problems with signal dropouts, and a reduced chance of success when playing on another machine, or if the tape stretches or shrinks slightly.