What is the difference between a BMW 325i and a BMW 325is?

This depends heavily on the year of the 325is. The "s" designates "sport", and it typically has been collection of performance options.

The original 325is was introduced in 1987 with the "e30" body style. That generation of 325is was specially the 2 door sedan (other makes refer to this as a "coupe", but BMW calls it a 2 door sedan) with a firmer suspension, limited slip differential, special air dam, trunk spoiler, sport seats and other upgraded interior features. Later generations had similar upgraded options that are year-specific, but always include performance options (firmer suspension, LSD) and the high-end interior options (sport seats).