I am late for school vs I am running

Some examples from the web:

• I am late for school
• I am late for my bikini wax.
• I am late for a breakfast meeting.
• Annie, I am late for a polygraph.
• Boy, I am late for that meeting.
• Yes, and I am late for court.
• Olivia, I am late for work.
• I am late for the African orphans.
• And I am late for rounds.
• I am late for an event.
• I have a thing that I am late for...
• I am late for my bikini wax. Hurry, please.
• Now if you will excuse me, I am late for my daughter's arranged wedding.
• And I have to run because I am late for a meeting with an old friend from L.A.
• And I have to run... because I am late for a meeting with an old friend from L.A.
• Now, if that's it I am late for an appointment with my attorney.
• that I am late for an appointment.
• Of course, but right now, I have another meeting that I am late for.
• Now, if you'll excuse me, I am late for my evening plans.
• Okay, I am late for a photo shoot.
• But right now, I am late for rounds with my new boss.

Some examples from the web:

• My name is Langston Jefferson Battle Ill... and I am running for the United States Congress.
• I am running for governor of the great state of Illinois.
• I am somewhere in the jungle in Thailand and I am running for my life.
• And now, ten years later, I am in love with one beast and I am running from another.
• I am running in order to catch the train.
• I'm not running away from things, I am running to them.
• I am entering the race for town council, and I am running against you.
• I am running a bath for Marilyn.
• And I am running the registration on the third car now.
• This is why I am running for president... to shut down these mines.
• I am running a trace now.
• But the nature of the operation I am running is not.
• I am running for Senate now.
• At the moment I am running two households.
• If that's sarcastic, I am running late.
• I am running away from something frightful and cannot escape from it.
• And not to sound cold-blooded, but I am running a business here.
• I am running through every variation of the neurotoxin antiserum.
• Agent Shea, I am running this investigation.
• I am running for the most powerful office in the world.