I'm more referring to unit differences in this case. That said, you bring up a good point. I've seen "Dates" and "Durations" (or some variant of the term) used to resolve that pretty successfully, yeah. Unless you're referring to times being fully unit aware in general, such as being able to call "TimeDelta.seconds", then that's another way to do it, but it's significantly more heavyweight. You need a bunch of static factories for each measurement and such.
As far as being unit-aware, you could probably just get away with providing a robust interface for working with multiple units. For instance, the type could store everything at the highest resolution you care about internally (milliseconds, microseconds, etc.), and any overloaded operators would operate in that unit, but expose an interface for operating in other units. Think TimeSpan and DateTime from .NET.
I'd say the hardest part is making sure all your engineers actually remember to use the special time types instead of raw integers