I was at a local music store and was asking about mixers and they suggested a small pre-amp instead with volume control. What is the difference between the mixer and the pre-amp? Is it just the controls?

With a mixer you can mix incoming audio channels, preamp just amplifies the low level mic signal to line level.

A basic (but very good) mixer like Sound Devices 302 has 3 input lines which you can assign to 2 output channels. Like mic 1 to channel 1, mic 2 to channel 2 and mic 3 to both 1 and 2, or whatever, and set all mic level individually. With larger mixers you can also pan the incoming mic lines to output channels as you wish.

The idea of a mixer is to make possible to use greater number of mics or incoming line level signals than there are channels in the final recording medium, usually 2 channels with video. Good mixers like SD302 also have good limiters, test tones, many different ways of monitoring the signal, good meters etc.etc.

I use a mixer even with one or two mics just because of the limiters and meters. More work setting up the shot, but MUCH more peace of mind.

There can be a big difference in the quality of outboard pre-amps compared to the ones that they throw in cheap mixers. Dedicated pre-amps almost always sound at least a little better than your average mixer.
One of the bigger differences could be in "headroom" or the amount of volume that the pre-amp can handle. A good pre-amp is a safer bet if you are working with unpredictable (soft and loud) sound sources.
Unfortunately, price doesn't always mean better. Let me bore you with a little story to illustrate.

I was taping a violin recital using a high end Focusrite 2 channel pre-amp(almost $600) I put on my headphones 20 minutes before the show continously monitoring the ambient noise to make sure everything was working fine.
As the group of violinists enter the back of the room and make their way to the stage, one channel goes completely DEAD! I promised a quality Stereo recording, and now I have mono.
I pulled out the trusty 4 channel Berhinger mixer ($39) that I carry around for emergencies such as this and had it hooked up to my XL1s by the end of the first (very short) peice.

The moral of the story is, yes the Focusrite sounds way better then the Berhinger, but the client never noticed the difference. The other moral of the story is, always carry backup!

Mark

I've done several short movies booming straight into my FR2 pre-amps. I recently added a SD302 into my kit. This creates far more versatility (I can feed camera and recorder) and I can fix the gain on the FR2 and feed it with the optimised signal from the 302 and never worry about the FR2 clipping since I've done a full scale calibration. The 302 also has a far superior I/O limiter built in, and the rumble cut-offs are before the pre-amps, not after. Which means clipping is even less likely.

Is a pre-map mixer necessary on a short film? Not strictly necessary. Just as white balance for the camera is not strictly necessary for the pictures to be recorded .....