You are correct. The all mountain bikes are heavier, have more travel both front and rear, and do have a different geometry. They' in between a trail bike and a downhill bike - good for free-riding.
A cross country bike will be lighter and have less travel (but likely enough for what you will be doing). I currently have a cross country bike, but have had both. I race, so prefer the cross country, and can still manage any type of free ride-type stuff I want to do (which is limited). Would I ride this down a mountain? Yes, but not on downhill-specific trails, likely.
Try both, but that should help you clarify the differences.
SheFly
ETA: the travel difference is usually 1". A cross country will have 4" vs 5" for an all mountain, for example...




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