Distinction if any between Pressure/Vacuum relief Valves and Breather Valves.
Breather Valve  = Pressure Relief Valve + Vacuum Relief Valve,A Breather valve for a tank requiring IN-breathing and OUT-breathing is normally called a Conservation valve.  Such a valve consists of a vaccum valve + a pressure valve as indicated earlier.  A Breather valve is required for thermal changes.  Instead of calling them VALVES, we normally call then VENTS.
As long as you understand how to size these valves (or vents) and how to search vendor catalogs for what you want, don't get too hung-up on terminology.  Some vendors even refer to some vents as relief valves!?!First, I have not had any direct experience with floating roofs; but I have a lot with fixed roof tanks.  The purpose of floating roofs as I undertand them (with out refreshing my memory of API practices) is to allow the roof to move to compensate for in-breathing and outbreathing and therefore they do not require separate vent devices for breathing purposes.  IS this what you understand?
Next, I think you are saying you have a fixed roof tank, where you cannot vent out toxic gases.  In this case a condenser to collect condensate is appropriate, with the remaining vapor being sent to a recovery system or flared being typical.
Also, another method of reducing process vented vapor may be to pad the tank with nitrogen and continuously vent this nitrogen; this would be a good application if you wanted to also prevent the ingress of air into the tank.
The above would take care of normal operation.
Again, I'm not sure I'm ansering your question, but a breather vent, conservation vent, pressure vent, or vacuum vent (or substitute valve for vent) are all designed in a similar way.  They usually have either a weighted pallet or the pallet is spring loaded.  Therefore, there is not a techical difference between them.  But there is a big difference between these pallet like devices and RELIEF VALVES!  R/V's are more expensive, and have a huddling chamber which permits the valves to pop open.  R/V's are a sonic flow device in that sonic flow normally occurs at the orifice,  Vents or valves with pallets are a sub-sonic device.
For API desinged tank we use pallet-like devices, for ASME vessels, piping and other process installation we use relief valves, rupture disks or rupture pins - usually in that order.

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