"at the plan time" and "on schedule" generally don't mean the same, even thought in some case it can mean the same.
Let me start with "on schedule":
This phrase is very straight forward, It has the same meaning as "on time", and both mean "按照預定時間" or "準時". For examples:
The airplane has arrived on schedule .
All the attendants have arrived at the meeting room on schedule.
The package has been delivered on schedule.
However, "at the plan time" can mean differently in different sentence, for examples:
This project at the plan time (在計劃時) encounters lots of obstacle.
The locomotive has delivered to railroad administration at the plan time (as planned, here it has the same meaning as "on schedule").
The house development begins at the plan time.
But because of the commitment at the plan time , teams have to do this to keep the promise.
2012-03-13 14:06:37 補充：
I like to bring your attention for "at the plan time".
To make the statement clearer, it is better to use "at the planned time" = "on schedule", or "during the planning time" = "the planning process is ongoing".
2012-03-13 14:07:38 補充：
The reason is "at the plan time" is NOT very specific, and it leaves the ambiguity for the meaning of the sentence.