No, they are not the same.
Production Red is similar to a Rhode Island Red or a New Hampshire: the males and females are both red, and they usually have some black in the tail. You can breed them together and get more of the same.
Red Sexlink has red females and white males, so you can sex the chicks by color.
They are a hybrid (cross of two breeds), and you breed them to each other you get chicks where either gender can be either color (and a few other color combinations too.)
Red Sexlink females usually have white in the tails and around the neck. This is not required to make the sex-linking work, but is common because of what breeds are usually crossed to get them.
Where did you get them? Feed stores are notorious for mis-labeling chicks, but I know that some hatcheries sell sexlinks with black tails and many hatcheries sell sexlinks with white tails.
Yes, but they are much less common than Production Reds.