Hi David,
The battery rating 110/85Ah primarily referees to the size or capacity of the battery. In simple terms a fully charged 110A battery can supply 1Amp for 110 Hours or 110A for 1 hour. and the same process applies for the 85Ah battery. in practice it is a bit more complex than that but its good enough for this explanation.
All batteries will have a maximum current output rate. What it is depends on the individual battery design. Car batteries are often designed to provide 400 to 600 A peak current to start the car, Leisure batteries are designed for a less demanding output, but most should cope with the peak demand of your mover without distress.
The two figures for the current the mover uses relate as follows.
The 120A is effectively the stall current. The mover uses this amount of current for a small fraction of a second whilst it actually begins to turn the motor. as soon as the motor is turning the current very rapidly drops to some thing close to the lower value of 20A All this happens within less than a second, unless the wheel is jammed and it cant move.
Most movers are only normally needed for a few minutes just to position the caravan, most times it is less than 6 min. in total. 6 mins is one tenth of an hour, so if it was using 20A for 6min. that equates to only 2Ah power usage plus a bit for the starting current which should be negligible compared to the power used whilst actually moving, because of its very short duration.
By comparison, if you run your 12V reading spot lamp for 1 hour you will use a similar amount of power! so an 85ah battery should work quite effectively for you.