Custom taxonomy assigned to cpt not showing in front end

Hi,

I have assigned a custom taxonomy to post types. It is there in the admin area. Great!

But it's not there in the front end.

I tried adding the custom field taxonomy. It shows now in the front end, but in the admin area there are two fields for the same taxonomy.
I noticed that the taxonomy assigned to the post type drives the archive lists, the one entered as custom field does not.

Question: how to get the taxonomy assigned to the post type available for input in the front end?