Mostly the difference would be between the armor level of the target and the speed. Tanks move relatively slowly compared to planes/helicopters and are very heavily armored. So they require a different warhead, usually a shaped charge or something armor piercing.
Planes/Helicopters move very fast and are pretty maneuverable, but are usually pretty lightly armored. An anti-tank shell or missile would certainly destroy a plane if it hit it, but are often much slower and less maneuverable than an anti-air weapon. Anti-air weapons usually have more of a shotgun style warhead to basically pepper a plane with shrapnel instead of having a “direct hit”.
So to sum up: most anti-tank weapons would certainly destroy an aircraft if they hit it, but would have difficulty hitting it. And most anti-air weapons could probably hit a tank, but likely wouldn’t cause much damage.
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