PROBABLY the difference does not matter.
There is very little chance that the very high capacities claimed will be genuine in a cell / battery that size.
2200 mAh is more capacity than you'd expect in a LiIon CR123xx battery.
They may just be lying about capacity - which is common - and it may be an OKISH LiIon battery.
But it may be higher capacity but not rechargeable as it is a Lithium "primary" cell.
And often enough when people claim VERY high capacities they are liars selling junk and the products are LOWER than usual capacity.
Trying to recharge a Lithium primary battery will not produce recharging but also PROBABLY will not cause major damage. It is possible that it could cause fire or damage the charger in some cases - so do be sure that the batteries you use are rechargeable ones.
A fully charge LiIon battery will measure about 4.2V open circuit and should never be discharged below about 3V minimum.
There is a small chance that if you has a charger designed for a 800 mAh LiIon cell and you tried to charge a GENUINE 2200 mAh LiIOn cell with it that you could have problems - but in most cases the battery would at worst take longer to charge. It would also terminate charging at a lower percentage of its rated max charge current (as the charger was charging at 800/200 of fullcharge and shutting down at say 25% of this). The effect of this would be to charge the battery to slightly more capacity than a proper 2200 mAh charger would, but this wou;ld be unlikely to be a major problem.