No, proper time is not the rate at which a clock ticks as observed by an external observer. Proper time refers to the time interval measured by a clock that is at rest or moving uniformly in a specific reference frame. It is the time experienced by an object or observer in its own frame of reference.
On the other hand, an external observer who is in a different reference frame will measure a different time interval for the moving object due to time dilation. Time dilation occurs when two observers in relative motion measure different time intervals due to the relative velocity between them. The observer in a different frame of reference will perceive the moving object's clock to be ticking slower compared to their own clock.
So, proper time is the time experienced by an object or observer in its own frame of reference, while the time observed by an external observer is affected by time dilation.