I've heard both these terms used when describing the behavior of a part when switching between two reference clock sources. Are they similar?
These two terms have different meanings, but they are often confused.
When a clock device performs either a hitless switchover or phase build out, then the output will not exhibit any runt or extralong pulses.
With hitless switchover, the phase of the output will change in a tightly controlled manner as the internal PLL locks to the new reference input.
When a clock device is set for phase build out, then the output phase will not change at all, even if the new reference input is not in phase with the prior reference input.