You can use [`Tuples`](https://reference.wolfram.com/language/ref/Tuples.html):

    Tuples[f[{a, b, c}, {a, b, c}]]
>{f[a, a], f[a, b], f[a, c], f[b, a], f[b, b], f[b, c], f[c, a], 
 f[c, b], f[c, c]}

    f @@@ Tuples[{a, b, c}, 2]
> same result

    Tuples[f[{a, b}, {r, s, t}, {x, y}]]
>{f[a, r, x], f[a, r, y], f[a, s, x], f[a, s, y], f[a, t, x], 
 f[a, t, y], f[b, r, x], f[b, r, y], f[b, s, x], f[b, s, y], 
 f[b, t, x], f[b, t, y]}

    f @@@ Tuples[{{a, b}, {r, s, t}, {x, y}}]
> same result

    p = {a, b};
    p1 = {a, a, b, b};
    Tuples[f[p, p1]]
>   {f[a, a], f[a, a], f[a, b], f[a, b], f[b, a], f[b, a], f[b, b], 
     f[b, b]}