I've worked in a restaurant for 7 years and have heard every variation of, "Well done, I don't want no blood left in that steak." and "This isn't cooked, there is still blood." that you could imagine.
So what is that red liquid you are seeing in red meat? Red meats, such as beef, are composed of quite a bit of water. This water, mixed with a protein called myoglobin, ends up comprising most of that red liquid.