What's the difference between "run towards me" and "come running towards me"?

1. Can I change "came running towards me" in the following sentence into "ran towards me"?
2. "come running to me" implies "start to run to me"?

I crossed the street to avoid meeting him, but he saw me and came running towards me.

Question

What's the difference between "run towards me" and "come running towards me"?

1. Can I change "came running towards me" in the following sentence into "ran towards me"?
2. "come running to me" implies "start to run to me"?

I crossed the street to avoid meeting him, but he saw me and came running towards me.

Answer

It doesn’t imply ‘start’.

He came towards me. (The action is ‘coming’)
He came running towards me. (The action is ‘coming’, ‘running’ tells you how)
He ran towards me. (The action is ‘running’)

In your example, the main idea is that he ‘came’, not that he ‘ran’. ‘Came running’ sounds a little more natural.