Hard glass if often known as Pyrex. It indeed is borosillicate glass. The first mercury lamps using borosillicate glass often had a name designed around the concept of the better temperature resistance of this kind of glass. For example, the first Westinghouse lamps made with hard glass had the "WeatherDuty" brand.
Basically borosillicate glass will withstand higher and quicker thermal shocks without flying apart.
And tempered glass is treated with a precisely controled thermal shock that makes it stronger instead of breaking it.
