Show terms in archive page

get_terms() retrieves terms in general, it makes no connection to a current post in loop.

What you need is one of template tags, which retrieve terms for the post. For example the_terms():

while (have_posts()) : the_post();

      the_terms( get_the_ID(), 'event_cat' );

endwhile;

There are quite a few functions dealing with terms, depending on what you want to do with data.