Q: Does the word "connect" mean the same thing in "This computer will connect well to the network." and "Our computers connected."?

A: the same meaning

Q: Does the word "cup" mean the same thing in "He drank a cup of coffee." and "He borrowed a cup of sugar."?

A: the same meaning

Q: Does the word "grace" mean the same thing in "I'm so grateful to God for the grace that He has given me." and "God's grace is manifested in the salvation of sinners."?

A: the same meaning

Q: Does the word "comfort" mean the same thing in "His friendship was a comfort." and "A padded chair was one of the room's few comforts."?

A:
the same meaning