I fail to understand the difference between stamina and vitality gains a potion provides.
For example, which one provides quick health regeneration when applying swallow?

Vitality is health. Stamina is the ability to keep doing things: exertion. If Geralt is slow or unresponsive, his stamina is low or depleted. If he keels over and dies, his vitality is spent.

What he said...

But to expand - Health is the large red bar on top. You lose health when struck, poisoned or out of breath. At zero you die. Eat food to regain health and health potions like Swallow will allow you to regain it slowly. Most players will have a food item (like Chicken) slotted in the R slot so they can quickly grab a bite when low on vitality.

Stamina is the curved yellow bar underneath. It needs to be full to cast signs. It regenerates on it's own out of combat and more slowly in combat. Tawny Owl potion prompts it to regain quickly, even in combat.

Note that the Superior Tawny Owl does not expire between 6PM and 7AM - giving an advantage to fighting at night.

Have fun!

Thank you Hickory and Peetz for clearing this up.