Hey,
SMPTE - Society of Motion Picture and Television Engineers, this is a group of people who deal with the technical sides of movies and tv. A few years back (1980 I think) they came up with a way to allow people to sync up video and audio machines using SMPTE sync, it is a series of quick audio pulses that can be transmitted and read from a tape by certain machines to master or slave playback between them.
You would use SMPTE to transfer information between two analogue tape or video machines so that their positions and speeds were accurately reproduced. In a digital world where you want to SMPTE sync and analogue source with a digital source, you would use MTC (MIDI Time Code); this requires a special device which reads the incoming SMPTE pulses and converts them to digital MTC.
SMPTE is not as accurate as a digital syncronisation signal, but it does a pretty good job. If you don't know what it is, you probably don't need it right now.
SPDIF - Sony Phillips Digital Interface, this is a type of digital audio connection that looks like an RCA plug, you can transfer audio digitally across a SPDIF connection from one device to another, like from a sampler to a computer. If any of your audio hardware has SPIDF outputs and your soundcard has a SPDIF input, you would record onto your computer using SPDIF cables.
Take care,
Nick