Why do indices behave differently than setting to a variable in bash loops over arrays that contain quotes and spaces?

Both quoting and word-splitting are affecting the result.

When double-quoted, "${samples[@]}" expands each array element as one word, and each word is double-quoted. Then the word-splitting for operation gets to see that sequence of words.

If you hadn't used variables it would be as if you had did the following, and for sees three words:

for each in "one 1 uno" "two 2 dos" "three 3 tres"; do

When not double-quoted, ${samples[@]} expands, but does not double-quote the words. So it's as if you had did this:

for each in one 1 uno two 2 dos three 3 tres; do

The for operation sees nine words.

Bill has explained how the for processes "${samples[@]}" (double quoted) and ${samples[@]} (no quotes).

In your case you can use both approaches to obtain the desired result:

i=0
for each in "${samples[@]}"; do                    # do not word split array elements
    echo "$i -----------------"
    echo "    ${each}"
    for item in ${each}; do                        # do word split an individual array element
       echo "    just the first: ${item}"
       break                                       # break out of loop after we process the first item
    done
    ((i++))
done

This generates:

0 -----------------
    one 1 uno
    just the first: one
1 -----------------
    two 2 dos
    just the first: two
2 -----------------
    three 3 tres
    just the first: three