For delta to be exactly 50, it means that N(d1) = 50 -->d1 = 0, which solves that s has be below k by a discount factor involving r, t, var/2. Therefore, delta isn't 50 for spot or even slightly different for atm forward
M-maybe. Or your statement could be overly strong. Delta is actually a predictive rate of change of the option relative to the underlying. Actual mileage may vary (and does) because price is set by actual B/A and TnS. I've frequently seen OTM options move far less than their deltas would suggest.
That occurs when a stock goes up, IVol drops, so OTM calls often do not match their delta. Then you have to take into account decay.