Compactness and sequential compactness are equivalent in metric space but not always in others

Question

There are many discussions about such question; however, they are proof-type answer

1. Compactness and sequential compactness in metric spaces
2. If $(X,d)$ is a metric space then I want to show that limit point compactness and sequential compactness are equivalent.
3. Compactness and sequential compactness

Could anyone use a simpler description to guide me that when both of them are equivalent and when they are not?