In the olden days, Over voltages produced due to lightning acted as a severe threat to the power system. So the device which was used to suppress this lightning over-voltage was termed as lightning arrester.
But in the recent times due to the development in power system, EHV and UHV systems came into existence. Thus the effect of Switching over-voltages ( due to the opening and closing of circuit breakers) is much severe when compared to the Lightning Over-voltage.(as the transmission line voltages have multiplied by many folds)
Thus they have re-framed the word as Surge arrestor as it has to arrest both lightning and as well as Switching over voltage. Basically, both the lightning arrester and surge arrester are one and the same in construction, operation and in everything.