Also raises type_error if Arg is not compound:

?-
arg(1,foo,X).

ERROR: Type error: `compound' expected, found `foo' (an atom)

An example for "backtracking yields alternative solutions"

?-
arg(Position,f(a,b,c),Term).

Position = 1, Term = a ;
Position = 2, Term = b ;
Position = 3, Term = c.

The operator to decide whether "it's the same" is unification, not "==":

?-
arg(Position,f(A,B,C),X).

Position = 1, A = X ;
Position = 2, B = X ;
Position = 3, C = X.

?-
arg(Position,f(A,B,C),B).

Position = 1, A = B ;
Position = 2 ;
Position = 3, B = C.

A bit abstrusely:

?-
arg(Position,f(a,K,h(K)),K).

Position = 1, K = a ;
Position = 2 ;
Position = 3, K = h(K).

?-
set_prolog_flag(occurs_check,true), arg(Position,f(a,K,h(K)),K).

Position = 1, K = a ;
Position = 2 ;
false.

The above also means you can search:

?-
arg(Position,f(a,b,c),b).

Position = 2 ;
false.

Excellent!