They both means have.
In the song https://www.youtube.com/watch?v=gk3VQoAKMUI
有 is used first in ni wen wo ai ni you duo sen.
Latter it's followed by wo de qing ye sen
Why use 有 and then use 的?
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有 is a verb which means "to have":
I have a glass of water
Wǒ yǒu yī bēi shuǐ
My name is Emily
Wǒ de míngzì shì Emily
的 is also used after adjectives:
hóngsè de píngguǒ
In songs, a lot of poetic license is used to maintain rhythm. So they're often not a normal way of speaking. In the following case there's probably a few ways of parsing the grammar. I interpret it as a kind of topic-comment sentence:
You ask: "I love you" has how much depth?
Nǐ wèn wǒ ài nǐ yǒu duō shēn
In the following, the possessive particle 的 turns 我 ("me") into 我的 ("mine"):
My emotions [are] also real
Wǒ de qíng yě zhēn