Even I found these explanations a little confusing, and some of the information isn't quite right, so I'll make it simple:

KBPS (MBPS,GBPS)= kiloybits (megabits, gigabits) per second, this is used to measure bandwidth in connection speeds in internet connections, network speed, or transfer speed of local storage.

KB/s (MB/s, GB/s)= Kilobytes/Second. This is used to measure downloads BECAUSE the file you're downloading is measured in bytes not bits. This allows you to understand the progress without doing conversion.

1 kilobyte is 8 kilobytes, so if you have a 64kbps you'll be able to download 8 kilobytes per second (today 8mbps = 1mb/s is more relevant).

I just noticed that this was bumped from a VERY old post, but I'm already done typing so I'm going to hit reply...