(Capacity 20hr: 65AH) Does this mean 65amps per hour for up to 20 hours?
No, it means that you'll get a total of 65 amp-hours out of the battery when you discharge it over a 20-hour period. This would correspond to a current of

$$\frac{65 \text{ amp-hours}}{20 \text{ hours}} = 3.25 \text{ amps}$$

during the 20-hour discharge.

Battery capacity usually varies with the discharge rate (current), so for comparison purposes, a standard testing period is specified &mdash; in this case, 20 hours.

With higher currents (shorter periods), you'll measure less total capacity, since more energy is wasted in the battery's internal resistance. With lower currents, you'll measure somewhat higher capacity, up to some limit determined by the the construction of the battery.