The Smith family lives in Canada. 'Family' is the subject, which is singular. The Smiths live in Canada. 'Smiths' is plural.

In American English, the word "family" is usually singular: "The Smith family liveS in Canada." I hear that in some varieties of English, "family" may be plural: "The Smith family live in Canada." In American English, "family" is only plural if you are thinking about the different members of the family. Compare: The Smith family has the biggest house on the block. The Smith family argue a lot among themselves.