The capacity of a Black Soul Gem and Grand Soul Gem is 3000, so when I go to enchant, is there a difference on how high the enchant is?

Are there other ways of getting a high enchantment other than have high skill, perks, and Grand Soul?

I've never enchanted, but my understanding is that Black Soul Gems are just Grand Soul Gems that have been modified to be able to catch the souls of the player character races. I would imagine they work just the same.

They are identical

Yep identical. Only black souls are from humanoids so they're super easy to get.

They are only different because the Black soul gem can contain human,mer, or the beast races souls. Other than that they are the same.

They are the same for enchanting purposes. The only advantage of black soul gems is that it's probably easier to capture human souls. You can also get higher enchantments through alchemy.

Wait, how do you do this through alchemy? Can you explain? Is it permanent is the important question for me?

By drinking Fortify Enchanting potions while enchanting.

I must have done it wrong, I drank a potion that increases bow damage by 20% for 60 seconds just seconds before I opened up the enchanting table and it still only enchanted for 40%. Is there a different potion I should use?

There is a potion literally called Fortify Enchanting. Drink that, and for X seconds enchantments you cast will be Y% stronger.

The boost to your Enchanting skill is temporary. Enchantments put on items in the meantime are permanently higher than they would have been if you hadn't drunk the potion.

Hehe, that would work perfect if you were trying to kill someone while standing at an enchanting table with your bow.

:facepalm: