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

Open the door a crack.

We managed to squeeze through a crack in the rock wall.
Answer: the same meaning
Question: "union" used in the same way in the following two sentences?

There is strength in union.

Let C be the union of the sets A and B.
Answer: different meanings
Question: "start" used in the same way in the following two sentences?

I start my day with a good breakfast.

The blood shed started when the partisans launched a surprise attack.
Answer: the same meaning
Question: "slot" used in the same way in the following two sentences?

Bob Dylan occupied the top slot for several weeks.

He put a quarter in the slot.
Answer:
different meanings