This kind of thing is something better handled in a partial. What you want is another file in your view directory like this:
_edit_links.html.erb
<%= link_to 'Edit', edit_conversation_path(conversation), class: 'btn btn-primary btn-sm '%>
<%= link_to 'Delete', conversation, method: :delete, data: { confirm: 'Are you sure?' }, class: 'btn btn-primary btn-sm' %>
Then in your conversation show (or whichever file you have there):
<%= render "edit_links" if current_user == conversation.user %>
Partials should be used when you want to split up the things on your show pages to make them more readable and/or maintainable. Helpers are useful when you have more complex methods that you call a lot. For instance, if you were checking if an object belongs to the person signed in multiple times, you might write a helper method like this:
def belongs_to_current_user rec
current_user == rec.user
end