Analog Camcoders(VHS,VHS-C,8mm,Hi-8) require an analog capture card in a PC. You connect it like you would to your TV or VCR. Digital Camcorders can used either the analog capture or have a direct digital conection to the PC(either firewire or USB).
With the digital camera and connection you will have a much better picture quality than the analog.
Most new digital cameras will record short video clips(don't know if they include audio). Length depends on memory size. My son's will record up to 98 sec on a 16MB memory card. I think this can be moved to the computer digitally over the USB cable.
I have an analog capture card in my computer for my 8mm camcorder. Also my son has a digital camera.