What makes a weapon anti-air or anti-tank? Would anti-air be effective against tanks? Could we create one weapon that covers both, or even all possible targets?
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An anti-tank missile is trying to destroy a strong metal box that moves slow.
An anti-air missile is trying to destroy a thin metal box that moves fast.
Those differences change how you design the missile.
To take out the tank, the challenge isn’t how to hit the target. The target is incapable of taking evasive action since it’s really slow moving compared to a rocket. The challenge is how to take the target out once the missile gets there and has to deal with an object made of the thickest and heaviest metal alloys available, and all the important critical systems are on the inside of that box.
To take out the plane, the challenge is the reverse of that. The challenge IS how to hit the target in the first place – a fast moving thing that can really evade well and it will take most of the propellant just to catch up to it. Once you get there it doesn’t take very much of a punch to bring down a box made out of the thinnest available metal alloys designed to be light, with many of its really important critical systems exposed on the outside of that box anyway. Especially since you don’t really have to penetrate that box anyway- just do a little damage to the thin bits that stick out on the outside the box. It won’t fly right and gravity will do the rest of the work for you.
Thus anti-tank missiles tend to have a squatter, shorter shape than their anti-air counterparts and slower rocket motors, but with a more directly “punchy” payload. The anti-air missile is narrow and long, all about the speed and the “getting there”, less about the punchy payload once it does (any general area shrapnel explosion will suffice).
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