The first sentence, "I'm only 20 minutes away from school," most commonly means that the speaker's location is a 20-minute walk, ride, or drive from the school. It refers to the physical distance in terms of travel time. However, it does not specify whether school begins in 20 minutes. The urgency ("I have to rush") could imply that school might be starting soon, but the sentence itself doesn't explicitly state this. Context would clarify whether the speaker is referring to the start time of school.

It could mean either, although ‘I’m only 20 mins away from *the* school’ would make it clearer that you are on your way, and you will arrive in 20 mins.