Tail light (or driving light as you call it) filament should go out as the brake light comes on (at least it does on most cars I've played with). Sounds like you simply have one brake light out. Check the contacts in the housing and use a multimeter to see if power gets through. Sometimes a bulb can look good but have a busted filament too. If it was an earthing issue then neither the tail or brake light on that side is likely to work.