Is magic and science the same thing in Skyrim or would they be considered completely different? Also, what would be the equivalent of nanotechnology and tissue regeneration?

I've been trying to build a female scientist, and it's a question that's been bothering me.

Any suggestions would be greatly appreciated

"Magic is just science we don't understand yet."

In the Elder Scrolls-verse, I imagine them to be two halves of a whole.

They seem to be treated similarly. Magic is a force of nature in Mundus and so is studied, like science is in our world.

Related, the Dwemers were engineers/technologist who use "science" to build things. But their creations have a good amount of magic build in (for example soul gems powering robots).

And Alchemy is kind of the rough equivalent of chemistry in our world.

Magic is the name for a type of energy transfer and matter manipulation.
Science is the body of knowledge of things which are understood and studied. These two things are not in opposition in any way except when Magic is posed as some sort of intuitive, divine art which results solely from the favor of a higher being.

I suspect that a scientist would use magic but mostly Alchemy, mostly its Scholars and Mages who do research throughout TES, i thin your main 2 skills would be Alchemy and Alteration.

Actually i believe one of the reasearch notes about dwemer you find somewhere in skyrim says that the soul gem doesn't seem to be the source of power for the automatons

Yeah, I should have said that soul gems are somehow used in robots, I did not mean that they are necessarily as a power source (I worded my comment poorly). The soul gem might function as a kind of brain, or maybe it has some other function. But the soul gems seems to contribute to their operation.

That was the result of understanding the workings of magic and soul gems. Which is effectively science in the Elder Scrolls universe.

In addition, don't the Blackwood Company use somekind of great mechanical pumping machine to extract hist from the tree?

I bet Ol Sotha could have explained it well.

Well, 100 years ago, nanotechnology was essentially magic, as was tissue regeneration (even re-attaching limbs wasn't possible), and the technology 100 years ago is far more advanced then skyrim. But then again, skyrim has magic, which would probably stunt the development of convention medicine (why bother trying to cure cancer when you can brew a cure disease potion?).

I'm guessing a scientist would probably level up several schools of magic, alchemy and enchantment, and maybe some speech.