How to customize search results layout in the action bar ?

Hello altogether,

 

we have the following problem. We want to customize the search results layout (search functionality in the action bar), when choosing the search option “All”.

So far, I couldn’t find any setup area to adjust it. The only thing I could do was to restrict access to the record types for a role we do not use.

However, I cannot restrict access / visibility to record type Appointments not restricting access to record type Task because the system sees both of them as record type Activity.

And, if one of the users is admin, the restriction has to be done also to his role. However, again there is a problem. This means, the admin cannot create any of these records, in case there is a case, he needs this record type.