For rate equations, are AB+A vs 2A+B vs A2+B equivalent?

I.e. if the reaction is dependent on the concentrations of A, do all three of the above give rate=k[A]2.

I think they would NOT be equal as A is a concentration.

For example, if A=0.5 moles/L

- 2A=2*0.5=1.0
- A2=A*A (I think?)=0.5*0.5=0.25
- Note sure how to treat AB

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FYI, for some context, here is the problem I am working on

I can see the slow reaction in the bottom left box has A+2B - so it is NOT of the form rate=k[A]2[ B]

In the bottom right one we have 2A+B -> D+I , so the rate equation iS of the form rate=k[A]2B

However, in the top right one, We have A2+B -> A2B.

I do not know if this A2, where it is 1 molecule containing 2 A atoms is equivalent to the bottom right one where we had 2 moles of A)

Similarly for the top left one, I do not know what to do when it is AB rather than A and B separately.

Thanks for the help.