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Hybridization has to do with the number of bonds only while the shape of the molecule takes lone pairs into account along with the number of bonds. For example, a trigonal planar and trigonal pyramidal molecule both have a sp2 hybridization even though they are different shapes. They both have three bonds, but trigonal pyramidal also has a lone pair, causing extra repulsion to give it a shape nature more characteristic of a tetrahedron.
Hybridization is the concept that atomic orbitals can be mixed to form new hybridized orbitals that helps us explain experimentally determined molecular structures. Another way to think of it is that hybridization acts as an explanation as to why structures undertake the shape that they do, for instance explaining how carbon in CH4 forms 4 bonds via the formation of 4 sp3 hybrid orbitals (by mixing one 2s and three 2p orbitals) despite carbon's electron configuration of [He] 2s22p2 supposedly only allowing it to form 2 bonds.
All though hybridization does relate to VSEPR, its main focus is not about helping you draw the model. All hybridization does is illustrate how many areas of electron density there are in a specific molecule and those fields can either be a boding pair or a lone pair. You can use it to help with smaller molecules but it is not necessary and it gets really complicated when you have much bigger molecules(then it becomes pointless and just slows you down).
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