To me, "until what time" and "how late" seem to have the same exact meaning and can be used interchangeably. For example, the following pairs of sentences illustrate some usages that seem the same to me:
a1) Until what time were you at work last night?
a2) How late were you at work last night?b1) Until what time did you stay at work last night?
b2) How late did you stay at work last night?c1) Until what time did you work last night?
c2) How late did you work last night?d1) Until what time can I call you?
d2) How late can I call you?
Am I correct that these phrases are exactly the same? If not, why?