There is one other fundamental difference between an electronic and photonic band gap that has not been mentioned yet: In general, the electronic band gap results from an attractive periodic potential for the electrons, whereas the photonic band gap results from a repulsive effective potential. This explains quite naturally why a 3D gap for electrons can be observed everywhere in nature, but is difficult to realize for photons. If one imagines building a crystal  adding atom by atom, one starts with a discrete set of allowed bound states (thus, almost all negative energies are disallowed for the single atom! ), which splits into N levels for N atoms and finally produces a band of allowed states if N goes to infinity. Thus, the number of allowed states INcreases while the number of disallowed states DEcreases. In contrast, if one starts with a single dielectric scatterer for photons, all positive photon energies are allowed. Adding more scatterers leads to interference of the scattered waves and only if the scatterers are aranged properly, the interference is destructiv for waves with given energy and wavenumber, and photon states with this energy and wavenumber can be considered as 'forbidden'.

The concept of a band gap in the same in both cases. It is a range of energies for which no states exist, i.e. a particle with that specific energy cannot exist inside the band gap.

In a semiconductor (undoped) there are no states for electrons inside the band gap (=electronic band gap), so between the valence band and the conduction band. In a photonic crystal there are no states for photons inside the band gap (= photonic band gap). While the electronic band gap in semiconductors is a property of the crystal lattice (crystal structure, atoms, periodicity), a photonic band gap is usually created by a periodic arrangement of dielectric indices (distributed Bragg reflector or holes in a semiconductor membrane).

Recently, also phononic band gaps have been investigated. These are band gaps for phonons (=lattice vibrations) in the crystal.

Electronic band gap is a forbidden region of energy for electrons.the main reason for the existance of electronic bandgap is the periodic potential that present in crystal lattice. A free electron can have any energy but an electron in periodic potential can not.

The concept of photonic band gap also arises from the periodic variation of a quantity i.e., the dielectric constant. Photonic band gap is the forbidden region of frequencies for photons in the crystal. This band gap depends on geometry of crystal. one can alter the photonic band gap by varying its structural parameters. 

Adding defects to a photonic crystal also alters the photonic band gap in a similar way that doping alters the electronic band gap.

Electron band gap represents disallowed electron energies in a (periodic) semiconductor crystal, whereas photonic band gap represents disallowed photon wavelengths in a (periodic) photonic crystal. 

Expressed in an alternate manner, the electron forbidden energy gap results from disallowed electron wavelengths (energies) in a periodic array of positive and negative ions, whereas the photonic band gap results from disallowed photon wavelengths in a periodic array of high and low permittivity dielectrics. 

I'd add that there are few interesting difference between them. In a simplest form of a semiconductor, i.e. the bulk form the electron forbidden gap exists in 3D. Indeed, an orientation of a crystal lattice doesn't affect a presence of the band gap in any direction. Since most elemental (not man-made) semiconductors are found in the bulk form, one can say that the mother nature has done a perfect job!

When making photonic band gap (PBG) materials, we're struggling to be as good as the mother nature. To have a complete (or full) PBG, one has to have not only a 3D periodicity of high and the low values of the dielectric constant, but the correct contrast between them and a certain lattice constant. To make things even more complicated, not any 3D lattice type will produce the complete PBG.

Very often structures will exhibit incomplete PBG (aka, stop bands) that exist only in certain directions in the photonic crystal lattice or for certain polarizations only. Hence, thorough modeling is usually required to predict optical properties before implementing such structures.

An idea of having a defect state in the band gap is equally applicable in both cases. For 3D PBG, it leads to a fascinating effect of light trapping or localization inside a PBG crystal. However, for 3D localization of electrons quantum confinement effects require structures like quantum dots (QD). (Quantum wells for 2D and quantum wires for 1D). The difference in the confinement scale (microns - for photons, nanometers - for electrons) is due to a difference in a wavelength associated with each entity.           

There is one other fundamental difference between an electronic and photonic band gap that has not been mentioned yet: In general, the electronic band gap results from an attractive periodic potential for the electrons, whereas the photonic band gap results from a repulsive effective potential. This explains quite naturally why a 3D gap for electrons can be observed everywhere in nature, but is difficult to realize for photons. If one imagines building a crystal  adding atom by atom, one starts with a discrete set of allowed bound states (thus, almost all negative energies are disallowed for the single atom! ), which splits into N levels for N atoms and finally produces a band of allowed states if N goes to infinity. Thus, the number of allowed states INcreases while the number of disallowed states DEcreases. In contrast, if one starts with a single dielectric scatterer for photons, all positive photon energies are allowed. Adding more scatterers leads to interference of the scattered waves and only if the scatterers are aranged properly, the interference is destructiv for waves with given energy and wavenumber, and photon states with this energy and wavenumber can be considered as 'forbidden'.