Question: "run" used in the same way in the following two sentences?

Nicklaus had a run of birdies.

The Yankees scored 3 runs in the bottom of the 9th.
Answer: different meanings
Question: "suffer" used in the same way in the following two sentences?

We hope you never have to suffer the same pain.

He suffered the penalty.
Answer: the same meaning
Question: "mean" used in the same way in the following two sentences?

I mean no harm.

I only meant to help you.
Answer: the same meaning
Question: "connection" used in the same way in the following two sentences?

The connection between church and state is inescapable.

The connection between overeating and obesity.
Answer:
the same meaning