If you put two 12 volt 80 watt panels together, the output will be 160 watts in full sun.
I don't claim to be an expert on all of this, but I'll explain as best I can:
First the units:
Amp; An amp is a unit of current, which means basically how many electrons are passing a given point, or more precisely, how much charge is passing a given point measured in Coulumbs per second, where a Coulumb is a specific quantity of charge, in the case of electric current, 6.241506×10^18 electrons (which is an incredibly huge number)
Volt; A measure of electrical potential or electromotive force based upon a charge differential between two points.
The Watt is a unit of power, that is to say that it is a rate of energy usage. It is defined as one Joule per second. Conveniently enough, if you multiply the current in Amps by the Voltage in Volts, you get the power in Watts.
Now, back to your panels. When you connect two panels, or batteries for that matter, in series, at maximum power, the current will remain the same, but the voltages will add.
Say your panel put out 1 Amp of current at 16 Volts at its maximum power point. This would be an output power of 16 Watts. If you took two panels and connected them in series, at the maximum power point, they would still put out one amp, however the voltage would be at 32 volts. The power would then be 1 Amp multiplied by 32 Volts, or 32 Watts.
Now, if we connected the same two panels in parallel, the currents would add and the voltage would remain the same. The voltage would be 16 Volts, and the current would be 2 Amps. The power would then be 2 Amps * 16 Volts, or 32 Watts.
For a real system, the way you connect the panels is going to depend upon the type of panels, charge controller, and the voltage of the battery bank you have. If you had a 12 volt battery bank and the same two panels used as an example above, and you were to connect them in series through a shunting type of controller, you would get about one amp of charging to the battery as the battery bank would pull down the voltage and for solar panels to match that of the batteries at around 12 volts. The current does not generally go up appreciably. If you were to connect them in parallel, you would get about two amps current into the batteries at 12 volts.
Now for your last question, if you were to hook two different panels up in series together, what would happen. Think of a plumbing system. The current would be analogous to the flow rate of the water, the voltage would be analogous to the pressure. if you have a section of 1/4" pipe connected on the end of a 2" pipe, the effect on the flow rate is going to be dominated by the 1/4" pipe. Well, for the solar panels, the panel with the lower current rating will only allow so much current to go through. You will get your 24 volts, but only at approximately the current rating of the smallest panel. About .83 Amps into your batteries in your case with the 10 watt panel limiting the current.
Hope this helps some, maybe someone can explain it a little better that I. Rich Hagen