In Boolean Algebra what is the difference between AB vs A.B notations?

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In Boolean algebra is AB the same as A.B and if not what are the differences between them?

And going along those same lines is C(A+B) the same as C.(A+B)

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Absolutely no difference other than the representation of $A\land B$ used to express "and".

We have other ways of representing $A$ and $B$, as you point out: $A.B = A\cdot B = A*B = AB$. In Boolean Logic $ A+B:=A\lor B$, and $AB=A\cdot B = A\land B$.

In computer coding, we often see $A\land B = A\&B$.

They are all various ways to express the conjunction, or the "and"-ing of two variables A, B.

Each context of study will emphasize one or the other, and a teacher in boolean logic will likely have a preference consistent with the text chosen for the class.