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See the following two images.

Formation of molecular orbital

Formation of sp hybrid orbital

I think that the two orbitals should not resemble each other because s and p orbitals overlap in different fashions in the two cases.

In the case of sp hybrid orbital, both s and p orbitals are centred at the same point. As a result, s orbital does constructive interference with one lobe and destructive interference with another lobe of p orbital.

But in the case of molecular orbital, s and p orbitals are centred at different nuclei (and those nuclei can't be at the same point). Then how come the resultant molecular orbital resembles the sp hybrid orbital?

The right lobe of the molecular orbital should get enlarged due to constructive interference of s and p orbitals, but why does the left lobe get diminished? Shouldn't it remain as it is in the p-orbital?

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It's important to realize that both of these drawings are highly stylized renderings of the electron density that are intended to provide a qualitative understanding. They don't accurately represent the actual shape of the orbitals. For example, $p$ orbitals are much rounder and taller relative to their length than we usually draw them. They are drawn elongated so that they don't cover each other up if you are drawing more than one on an atom. So the fact that the drawings of the $sp$ hybrid and the $p+s$ $\sigma$ bond look similar should only be taken to mean that they both have a bias of density to one side. You can't really conclude much else from the drawings.

The Orbitron website is a great resource for seeing the actual shape of the electron density of different types of atomic orbitals, which you can compare to the drawings.

MolCalc produces similar images of molecular-level orbitals. The bonding orbital of HF is probably the closest you can get to the $p+s$ $\sigma$ bond orbital in your drawing.

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The center of the positive nuclei is the same.

Imagine a line between the two nuclei in the sigma bonding MO. The nuclei in the sp hybrid orbital is to be found somewhere on this line.

This is the negative center of the orbital and naturally the spot where the positive nuclei will be. In the first picture there are two nuclei and their positive center (together) will be there too.

Hope I could help. English is not my native language.

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