Your intuition was right in that grams is mas, not weight.
The best way I’ve had it described is mass is a measure of how hard it is to get something to move. You have to push a 2kg thing twice as hard (over the same time) as a 1kg thing to get them to move the same speed.
Weight is a measure of how much things are attracted to each other through gravity and is a Force; not a mass. Since basically everything is miniscule compared to the earth we don’t really care how much each car is attracted to each other, but how much it is attracted to the earth is very measurable due to the earth’s immense pull.
Since we all live with the same gravity many use weight and mass interchangeably, but 1kg on earth is 1kg in space and 1kg on the moon. 1lb on earth is 0 in space, and like 0.1lb on the moon.
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