The address is the whole story. Aye ajnabi: O stranger. It is the politest word the language has for somebody who is not yours, and the entire song is addressed to her with that word. He never once claims her. He asks her to make a sound, from wherever she is, so he can know which direction she is in. That is the level of ownership this love song is built on.
The reason he asks is the second passage's business. Main yahan tukdon mein jee raha hoon, tu kahin tukdon mein jee rahi hai: I am living here, in pieces, and you are living somewhere, in pieces. The song does not say the pieces are each other's, but the two lines are built so that the reader fills it in. Two people cut into fragments, and each fragment has part of the other in it. That is the song's quiet version of the soulmate idea, and it is the saddest possible one, because fragments do not reassemble.
The next passage stops calling and starts looking. The silken wind, passing to and fro, asks him to say what he is missing: that bud, washed in milk, so innocent. Where is it. Where is the light. Where is the life-like one. The questions pile up without waiting for answers, and the last line of the passage stops being a question at all. I am incomplete, and you, incomplete, go on living. It is a description, not a plea.
The last passage is the one that earns the song its place in the film. You are not here, but your smile is. Your face is not here, but your footsteps are. Aahatein are the sounds a person makes moving around just out of sight, and the whole passage is built on them: she is present exactly the way absence can be, in traces. Then the questions start again and land on the hardest one. Mera jahan kahan hai. Where is my world. He has spent three passages asking where she is, and the song ends by admitting that he does not know where he is either.
Dil Se was the last film of Mani Ratnam's trilogy of the decade, after Roja and Bombay, and Gulzar wrote all of it. Udit Narayan and Mahalakshmi Iyer trade the passages between them, and the recording people mean is the one from the film.