sequences and series – Combinatorics terminology for list of options

I am currently working with lists of options, where the options are numbered from $1$ to $n_k$ and are ordered increasingly, where $k$ is the number of lists.

Question 1: currently I am calling these simply sequences, do these have a more specific name?

From these list of options, I am generating $k$-tuples, where the elements of the tuples are the options of the lists, in the order the lists have been defined so they have the same index, like this:
$S_1 = (1, 2, 3)$
$S_2 = (1, 2)$
$S_3 = (1, 2, 3, 4)$
All $k$-tuples:
$(1, 1, 1)$
$(1, 1, 2)$
$(1, 1, 3)$
$(1, 1, 4)$
$(1, 2, 1)$
$(1, 2, 2)$
$(1, 2, 3)$
$(1, 2, 4)$
$(2, 1, 1)$
$(2, 1, 2)$
$(2, 1, 3)$
$(2, 1, 4)$
$(2, 2, 1)$
$(2, 2, 2)$
$(2, 2, 3)$
$(2, 2, 4)$
$(3, 1, 1)$
$(3, 1, 2)$
$(3, 1, 3)$
$(3, 1, 4)$
$(3, 2, 1)$
$(3, 2, 2)$
$(3, 2, 3)$
$(3, 2, 4)$
The order of the tuples doesn’t matter, so the number of $k$-tuples become $n_1n_2…n_k$, in the example it is $3×2×4$.

Question 2: currently I am calling this combinatorial operation simply all possibilities, does this have a specific name?