Or is it?

Remember that there is no central atom here – the molecule is symmetrical; what happens to one carbon happens to the other. This means that the other carbon that has already formed a bond with our carbon of interest also has a 2p orbital free. I’ll give you one guess as to what happens between the 2p orbitals of both carbons.

If you guessed “they form a bond of their own”, you would be correct. Although this one is different, isn’t it? This bond wasn’t formed through hybridization, but more as a consequence of two atoms looking for an additional electron that the other one had. Now, I wonder where we discussed two different kinds of bonds before…

That, my readers, is the difference between a sigma and a pi bond. Each of the bonds formed during the hybridization process are direct, sigma bonds, where the last bond, formed simply by the nearness of the two atoms to each other, is a pi bond. Where each single covalent bond represents a sigma bond, the one double bond represents a sigma bond and a pi bond*.