As far as I know, they have always been two seperate games. Despite their similar concepts, they have a different look and feel to one another, Street Fighter is a more cartoonish and arcade style whereas Mortal Kombat has a more gruesome and realistic style. They were also made by different companies, Street Fighter was made by Capcom and Mortal Kombat was made by Midway.
Here are two wikis I found on them.
Street Fighter
Mortal Kombat