Isomorphism A to B or B to A?

Question

Let G and H be groups, and let f : G → H be a homomorphism. Then:

1. The kernel of f is a normal subgroup of G,
2. The image of f is a subgroup of H, and
3. The image of f is isomorphic to the quotient group G / ker(f).

In particular, if f is surjective then H is isomorphic to G / ker(f).

Source: wiki

Whereas in gallian for the third property it says "G/ker(f) is isomorphic to image of f"

Are both the same thing? A isomorphic to B iff B isomorphic to A?