First thing, users should be able to see the printers which are connected to their machines in only their sessions. So If user A has logged in Session 1 then he will see lets say 3 printers connected to his machines.
Printers in TS are redirected from the client machine. So if you have a print server on the LAN and users who have added the printer to their local machines will get the printer redirected in their session and when they log off then the printer will be deleted from the TS.
If at all you are seeing lot of printers in session 1 means that those must be stale entries. This generally happens when the user hive on the TS doesn't get completely unloaded. To resolve this you would need to install UPHClean tool on the Terminal Server. You can download it off the Microsoft Site.
Now to classify for home users and LAN users.
There is a setting in the options tab to redirect printers. If you enable it then all your printers will be redirected (Network printers + local printers) If you disable the option then no printers would be available. So you cannot actually specific which printers to redirect.