Variable in Array Not Working

PHP interprets those arrays differently. In the first example you’re asking WP_Query to get posts
by 3 term slugs and in the second example you’re assigning the array a value of 1 string. If we were to print the two arrays it would look like this:

Your Example 1:

'terms' => array(
    [0] => 'The A Team',
    [1] => 'The B Team',
    [2] => 'The C Team'
)

Your Example 2:

'terms' => array(
    [0] => '\'The A Team','The B Team','The C Team\''
)

PHP thinks that you’re assigning it a single string, even if there’s commas in the string itself it is an absolute string. What you’ll need to do is make the variable itself an array.

$my_term_names = array(
    'The A Team',
    'The B Team',
    'The C Team'
)

'terms' => $my_term_names