Difference between P(A,B) vs P(A∩C) vs P(A.B) vs P(AB) 
*

*P(A,B)

*P(A∩B)  

*P(A.B) 

*P(AB)


Above 4 statements looks almost similar to me. Can anybody define if there is any difference between above 4 and compare them in detail.
 A: $A \cap B$ is often abbreviated to $AB.\;$ I also, am unfamiliar with $A.B$, but I suspect you may mean $A\cdot B$, which would be equivalent to the other two. 
Then comma notation is very common with events involving random variables. For example $P(X \le 3, Y > 2)$ is common shorthand
for $P(\{X \le 3\}\cap \{Y > 2\}).$ I have not seen it used just
for letters as in $P(A,B),\,$ except for consistency in a discussion of random variables.
In summary, I think they are all the same, with the possible
exception of the one with the dot in period position.
Notes: 
(a) In older books, you may find $A + B$ as an abbreviation for $A \cup B$, and more recently, as an abbreviation for "$A \cup B$ where $A$ and $B$ are mutually exclusive". 
So that $P(A + B) = P(A) + P(B)$ as in Kolmogorov's axiom, without
elaboration.
But $P(A \cup B) = P(A) + P(B) - P(AB)$ is a theorem. 
Whenever you see $+$ between sets, you need to check the
context very carefully.
(b) The use of $AB$
for $A \cap B$ can avoid parentheses in expressions such
as $AB \cup CD = (A\cap B) \cup (C\cap D),$ because one takes
it for granted that $\cap$ written as a 'product' precedes $\cup$ in the order of set-theoretic operations.
