We are introduced to the first type of love in the very first scene. Duke Orsino feels intense passion for Olivia, which is really more of an obsession. We especially see his obsession for her portrayed in his lines describing that the moment he first saw Olivia was the moment his desires for her started hunting him and tearing him apart, the way dogs hunt and tear apart a deer:
O, when mine eyes did see Olivia first,
Methought she purg'd the air of pestilence!
That instant was I turn'd into a hart[deer],
And my desires, like fell and cruel hounds,
E'er since pursue me. (I.i.20-24)
Since his passion for her is an obsession, we know the love Orsino thinks he feels for Olivia is not the purest nor strongest kind of love.
A second kind of love found in Twelfth Night is the more devoted, more real kind of romantic love, which is illustrated by Viola's love for Orsino. We learn when we first meet Viola in Act 1, Scene 2 that Viola grew up hearing her father speak of Duke Orsino. Hence, we know she has grown up hearing him described as a good man, just as the captain describes him as "[a] noble duke, in nature / As in name (I.i.25-26). Therefore, it's not much of a surprise that she falls in love with him soon after entering his services, pretending to be a male servant. What's more, her love for Orsino is much more real than Orsino's love for Olivia because Viola's love is based on what she sees to be true of his character. In addition, Orsino grows to love Viola in return by the end of the play because he sees how she has devoted herself to him, even acting as his friend as she courts Olivia at his bidding while she is in love with him herself. Since he sees how devoted Viola has been to him, plus heard her proclaim that there is a woman who loves him as much as he loves Olivia, who turns out to be Viola, he very quickly asks her for her hand in marriage in the final scene of the play. Hence, a second kind of love found in Twelfth Night is the everlasting kind of romantic love that is based on knowing what a person's character is like and feeling devoted to that person.