Chicken and steak
Medium rare steak should have a warm, red center
The steak is more cooked through than very rare (please view "When cooking a steak what is considered very rare?"). The steak is cooked till it is still red and cool inside but, by cooking it so that the inside temperature rises to 120 allows the steak to have some flavor.
I ordered my steak medium rare and it came out well done.
A steak should be cooked how the person you are cooking it for likes it, you should always ask how the person likes their steak cooking. Some people like their steak rare, some medium and some well done.
Ronald Reagan liked his steaks well-done. I doubt that he hated rare steak, since he knew it could be cooked.
An under cooked steak.
Medium rare
The longest trend in the the steak house industry is to provide the juiciest, tastiest steak possible. Of course, this can include making them specific for the customer, like making it rare, medium-rare, etc.
Example sentence - The waiter asked if I wanted my steak cooked rare or medium rare.
The steak can be rare, medium or well-done. The eggs can be "up" (sunnyside up), "over" scrambled or poached. For example, you would simply say: "The steak medium rare, and the eggs over, please".
The word could be scarce.