This question usually comes up in reference to Acoustic Guitar equipment
because of what players read in manufacturers' sales copy when comparing
equipment before a purchase.
Some things are labeled "preamp", others "DI", and then others
Well, an integrated amplifier is any unit that houses
both a preamp and a poweramp. The poweramp deals with
current amplification, and the preamp deals with voltage
Therefore, an active DI is by definition also a preamp because voltage
amplification is occurring. That any particular active DI design
may or may not also feature buffering and/or equalization makes no
difference whatsoever; a preamp is a preamp.
Some devices are
specifically designed to boost while others are designed to attenuate.
When dealing with music equipment, there are so many more preamps than
just those in your mixer - they're everywhere!