A bit like 'standard orbit' which we hear in TNG and beyond and is never defined, perhaps space normal speed is reference to following a normal procedure for the type of space the ship is in, without resorting to on-screen technobabble.
Perhaps there are various 'speed limits' for different types of space, for example, joining or leaving orbit, where heavy space traffic is present, in proximity to asteroid fields / gaseous anomalies etc as well as interstellar space.
Re 0.5 warp, full impulse is significantly slower than lightspeed, and is not 0.99 lightspeed so if there is a need to travel at 0.5 lightspeed, the 0.5 warp would be the only way to do it. Also don't we only hear that during the acceleration phase anyway?
Perhaps there are various 'speed limits' for different types of space, for example, joining or leaving orbit, where heavy space traffic is present, in proximity to asteroid fields / gaseous anomalies etc as well as interstellar space.
Re 0.5 warp, full impulse is significantly slower than lightspeed, and is not 0.99 lightspeed so if there is a need to travel at 0.5 lightspeed, the 0.5 warp would be the only way to do it. Also don't we only hear that during the acceleration phase anyway?