Head Amp, exactly what do they do?

Well there are no bad questions.  So I hope this is not a bad answer.....  Basically your common amp consists of two sections, the amplifier, and the speakers.  Combo amps put both in the same enclosure and are the most common.  The alternative is to have the amp "head" as a separate component and the speaker cabinet(s) in it's (their) own cabinet(s).  Some "combo" amps will serve as an amplifier only component as well and have output jacks on the back to connect to other speakers to spread the sound around, or connect to a PA system, but in many cases connecting the external speakers turns off the on-board speaker.

Typically a "head" will have more output connection options for use, including different impedance loads, or possibly 70 volt out for powered public address type horns, so they certainly have their place out there.  As to which is better, depends on how you think you will put it to use. 

Hope that was slightly clearer than mud.
Thanks for asking "neighbor".

Take Care;
Doug

When you go shopping for amps, take a little time to anticipate where you are wanting to go with your music so that you get something that will adapt easily (and inexpensively) into the next phase.  Nothing like tossing cubic dollars into equipment that won't play well with the next thing on your list and ending up with a whole room of stuff that collects dust.

Personally I had considered a collection of pedals to get the sounds I wanted until I came across an amp that had all that on-board.
So now the thing just has a little midi controller to select the setting desired, and with a tap and bit of pressure on the expression pedal....  a whole board full of accessories became redundant.  To each their own, but for me it made sense to plug in one midi than hauling around the other.

Just something else to think about I suppose.

Take Care;
Doug

Well now the plot thickens...  depends on what kind of recorder you have on hand.  Usually the output from the amp is going to be rated at a given wattage, which may be far in excess of what your recorder is capable of tolerating.  Now from your latest statement, I gather that you have plugged your guitar into the input of your recorder directly and were able to record the product.  If that is the case, you can pretty much be assured that the recorder is looking for a fairly low power source (as your pickups generate a fairly weak output signal, similar to what you might get from a small recording microphone).  Feed it something around 59 volts at 10 watts + and something is going to make smoke.

For Recording an electric guitar, you would usually just Mic the speaker and rock on from there.  There is a reference document on the Shure website that has guidelines for doing that effectively.  Here's the catch though, now you have to buy a mic.  If your amp has a line level output, you can generally send that directly to a recording device because the output is tapped out of the circuit after the pre-amp stage and before the power amp stage.  It would still be nice to have some sort of output limiter on that anyway for the safety of your recorder.  When in doubt, always check the specs of the equipment to make sure that the output of one device doesn't exceed the input limits of the other.

I had an old electronics teacher that insisted that everything electrical had "smoke" in it....  if we screwed up, we didn't burn it up, but just let the "smoke" out of it.  Nothing beats the sound of popping capacitors and the smell of ozone first thing in the morning!

Take Care;
Doug