A question of having wide characters in an atom and a string:

?- S="s\u2200", string(S), atom_string(A,S), atom(A).
S = "s∀",
A = 's∀'.

A question of having ASCII characters in encoded form:

?- S="s\x5E", string(S), atom_string(A,S), atom(A).
S = "s^",
A = 's^'.

A question of displaying ' in an atom and a string:

?- S="s\'", string(S), atom_string(A,S), atom(A).
S = "s'",
A = 's\''.

?- S="s'", string(S), atom_string(A,S), atom(A).
S = "s'",
A = 's\''.

?- atom_string(foo, Z).

Z = "foo".

?- atom_string("foo", Z).

Z = "foo".

?- atom_string(Z, "foo").

Z = foo.

?- atom_string(Z, 'foo').

Z = foo.