You should use elseif for the second if statement:
$title1 = single_term_title( 'Conferences In ', false );
$title2 = single_term_title( 'CConferences In ', false );
add_filter( 'get_the_archive_title', 'my_theme_archive_title' );
function my_theme_archive_title( $title ) {
if ( is_tax('us_state') ) {
$title1;
}
elseif ( is_tax('country') ) {
$title2;
}
else {
return $title;
}
}
You can read here about true/false https://developer.wordpress.org/reference/functions/single_term_title/