If you remove everything from every human body except the skeleton, you'll find that the joints of every skeleton have very similar (nearly identical) range of motion. When I say design range of motion I'm referring to the commonalities that all of our skeletons share. The human skeleton has two arms, two legs, a hip bone, a skull, a spine, hands, and feet. Each of those are connected by joints and all of the joints have a range of motion that is, for all intents and purposes, the same. (Again, excluding birth defects, post-birth accidents, etc.)

On top of the skeleton we add muscles and tissues and everything else, with the muscles doing the vast majority of the supporting work for the skeleton, i.e., for the most part, the muscles (and tendons) dictate the effective range of motion, i.e., what the skeleton is currently possible of doing. But muscles can be stretched and lengthened, or they can be neglected and become stiff like an old rubber band (e.g., from sitting in the same position for years on end). Stiff muscles restrict range of motion, preventing the skeleton (which, without the muscles, would be fully capable of achieving its design range of motion) from achieving the full range of motion.

Are we all built to some universal specification? That depends on how you define "built" and how you define "universal". Our cells "build us" and our DNA defines a specification. Humans do follow a general standard: between 4.5-6.5 feet tall, two legs, two arms, one head, bipedal motion, etc. There are no 3-foot, 8-arm humans (like an octopus) and no humans with a 8-foot nose (like an elephant).

There are plenty of factors that can affect what range of motion each of us will be able to achieve, including injuries, age, and lifestyle (you're not going to become a world-class runner sitting at a computer for 12 hours a day 7 days a week), but if you're a relatively healthy 20-50 year old, and you put in the time required, you can go from being extremely stiff and inflexible to doing splits and backflips.