Answers for "how to get current post terms"

wordpress get taxonomy of a post

<?php $term_obj_list = get_the_terms( $post->ID, 'taxonomy_name' ); ?>

get taxonomy name in singhle post

// RETRIVE TERM SLUG ( for single.php or template-part )

$terms = get_the_terms( $post->ID, 'your-taxonomy' );
if ( !empty( $terms ) ){
    // get the first term
    $term = array_shift( $terms );
    echo $term->slug;
}