Remove[a,b,c,x,y];
a=1; c:=b; Block[{a=a,b=2}, x:=a; y=c];
?x
?y

Remove[a,b,c,x,y];
a=1; c:=b; Module[{a=a,b=2}, x:=a; y=c];
?x
?y

{x,b}

Remove[a,b,c,x,y];
a=1; c:=b; With[{a=a,b=2}, x:=a; y=c];
?x
?y