I know: Watts = Volts X Amps, but I need to know if I can use a 12V battery, 240Amps to power a water pump that's 12VDC/65Watts.

The pump will draw 5-6 amps, so it should run a while on each charge. A deep cycle battery would last longer.

Is your 240 - "Cold Cranking Amps (CCA)" or "Amp Hours"?

Deep Cycle Batteries are preferred as labman states.
The "Amp hour" rate of 240 loosely means 1 amp for 240 hours or 10 amps for 24 hours etc.

CCA is a measure of the maximum current it can deliver taking into account the battery losses like the internal resistance of the battery. CCA's of deep cycle battieries are usually less than the CCA of a car battery. Car batteries will be damaged if deep cycled.