1Ah might charge a car battery, but it will be a struggle... battery tenders for cars have a minimum 1.25Ah for a very gentle recharge without failing to do so... anything less works best for ATVs, alarm batteries, etcThey're not the same. The booster takes the place of another car when your battery is dead and you need a jump. It's not a trickle charger.
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I think the 1A (amp) means it will maintain the current state of the battery but not increase it. 2A will slowly charge the battery. When I put the charger on my battery after a couple weeks of normal driving (lots of trips less than 5 miles) 2A takes about 16 hours to bring it up to fully charged. 12A will charge the battery up in about an hour or less.
I would not try to recharge a battery at more than 7Ah as it will heat up the battery and hurt the cells