The "as-seen-on-TV" style don't use a battery, they run the fan direct from the panel, but this has certain, perhaps undesireable side effects - it takes more power to start a motor turning than it does to keep it running, so you would often see situations where you have good sunshine and the fan isn't running.
Have you considered where/how you'll mount that panel, keeping it safe from interfering fingers? If I put that on my vehicle & park in Georgetown there's a good chance it would not be there on my return.
Regarding the output voltage - solar or photovoltaic panels are a relatively high impedance power source - unlike batteries or generators - they are not constant voltage but constant current and output maximum voltage at minimum current, maximum current into a dead short, and maximum output (in terms of watts) at some point in between - if used to charge a battery (perhaps the most common use), the voltage measured at the panel output will be the battery's terminal voltage, and the current whatever the panel can deliver at that voltage, based on how intense the sunlight striking the panel is.
Charge control or regulation is typically done by disconnecting the panel from the battery (using a relay) to prevent over charge, rather than regulating the voltage to a fixed 13.8V, as the relay method is more efficient (more energy stored into the battery, less energy dissipated as heat). More sophisticated charge controllers use both techniques, switching from constant current mode/relay type control to constant voltage after the battery reached 90% full charge.
We used a device called a Linear Current Booster or LCB from Bobier Electronics to "impedance match" motor loads to PV panels if we weren't using batteries - mostly for solar powered water pump installations, again for effiency reasons, we stored water in overhead tanks, rather than electric energy in battery banks.