What is the difference between "to view" and "to see"?

Could you provide some usage examples when they both can be used and some in which only one of them is appropriate? In particular, which is better between "you can come and see the house" and "you can come and view the house"?

Along with @AlwaysAsking's good answer, I'd like to mention a bit of an idea of formality with regard to see versus view in the specific context requested.

A personal request to see the house will imply that the requester will show the house.

"Come see our house!"

Where as view is more formal and depersonalized.

"Come view our house."

It has an implication of inspection or examination without a personal level of familiarity. Whether or not the house is being presented/shown by the requester, it still is more formal and detached.

"To view" is usually used to imply that you are paying attention but "To see" does not always mean you are paying attention.

For example

She viewed the landscape.

means she was looking at the landscape carefully.

She saw him on street.

means she wasn't particularly following him or was looking for him (maybe she saw him accidentally.

In your example,

You can come and see the house

sounds more natural to me. If I want to emphasis that you can come and carefully see the house, I can use a stronger verb. For example

You can come and examine the house

or

You can come and inspect the house