What is the difference between dsp² and sp³d? Please explain with proper reason

Hybridisation is of various types depending on the types of orbitals involved.dsp2 and sp3d are also the type of hybridisation.In dsp2,inner d-orbitals participates and in sp3d outer d-orbital participates.
For ex- in [Ni(CN)4]2-In nickel the configuration will be 3d⁸,4s²,4p^0.But in the complex it is in +2 oxidation state thus configuration becomes 3d⁸,4s^0,4p⁰.When dsp2 hybridisation occurs one of the 3d orbital gets vacant by shifting its e- to the previous d-orbital thereby one 3d,one 4s and one of the 4p orbital gets hybridised forming four dsp2 hybrid orbitals.Now each of these orbitals receives a pair of electrons from cyanide ion,and the geometry will be square planar.Thus inner 3d-orbital is participating in the hybridisation so it will be dsp2 hybridisation.
Now in sp3d type of hybridisation the difference is that the outer d-orbital i.e 4d -orbital will involved not inner 3d ,thereby forming five-hybrid orbitals and the geometry will be trigonal bipyramidal.