∀x∃y(x≠y → M(x,y)) says that "if sender and receiver are different then send mail" that means sending of mail depends sender and receiver
1. if sender and receiver are different and mail also send then above statement is correct.
2. if sender and receiver are different and mail not sent then above statement is not correct.
3. if first condition is itself false then no meaning of looking for second condition that means statement is true.
∀x∃y(x≠y ∧ M(x,y)) says that "sender and receiver are different and send mail" that means sending of mail does not depends on sender and receiver, both conditions shold be true for making statement true.
so ∀x∃y(x≠y → M(x,y)) and ∀x∃y(x≠y ∧ M(x,y)) are different things.