Link under Player

Hello,

I wrote this before but I think I confused the person who was trying to help me out so I'm going to re-write it in another way. Hopefully it's understandable.

in the full node I would like the download link to appear under the player
in the node teaser I would just like to display the player

Is there a way to do this? I've been trying for months now and I'm about to give up unless someone let's me know how it's possible.

Thank you for you time.