The basic difference
A K-1 brings a fiance to the United States to marry within ninety days of arrival, after which they apply for a green card from inside the country. A CR-1 is a spousal immigrant visa: you marry first, then the spouse enters as a permanent resident, or nearly so.
What each one costs you in steps
The K-1 is two processes. The visa, then the adjustment of status after the wedding, with its own filing and its own wait for work authorisation. The CR-1 is one process, and the spouse generally arrives able to work without a separate application.
Where each one tends to make sense
The K-1 can suit couples who want to be together sooner and are content to handle the second stage here. The CR-1 can suit couples who can marry abroad and would rather arrive with status settled. Which is faster is not fixed, and depends on the post, the couple, and the record.
The ninety days are real
A K-1 holder who does not marry within ninety days cannot extend, and staying past it creates serious problems. Plan the wedding and the adjustment filing before arrival, not after.
