SGP is the first orbit propagator. It has been developed by Hilton and Kuhlman in 1966 thanks to one of Kozai's research work made in 1959. It is made for satellites orbiting near the Earth which includes satellites with an orbital period lower than 225 minutes. This model assumes that the eccentricity is low and that the perigee's altitude is constant.
SGP4 has been developed by Ken Cranford in 1970. It is an improvement of the previous propagator in order to track the growing number of satellites in orbit at this time. It is also used for near Earth satellites.
SDP4, developed by Hujsak in 1979, is the SGP4 propagator adapted for deep space objects. This includes satellites with an orbital period greater than 225 minutes. For period above this value, the satellite's orbit is disturbed by the moon and the sun, but also, by some resonance effects for orbital periods of 12 and 24 hours.
SGP8, also used for near Earth satellites, is almost like the SGP4 propagator but the calculation methods are different. However it follows the same models for the atmospheric and gravitational effects.
SDP8 is the SGP8 propagator adapted to deep-space effects. Moreover, SGP8 and SDP8 are better to manage the orbital decay.
Hoots, Felix R., and Ronald L. Roehrich. 1980. Models for Propagation of NORAD Element Sets. Spacetrack Report #3. U.S. Air Force: Aerospace Defense Command.
Vallado D. A; Fundamentals of Astrodynamics and Applications; McGraw-Hill, New York; 4th edition (2013).