What are the differences between heat cure and self cure acrylic resins?

Polymerization. Heat cure implies that heat is needed to accelerate or catalyze polymerization. Obviously it is not used intra orally since adding heat to a mouth is not comfortable or safe. Heat cured acrylics are used in makeing dentures which "cook" in hot water. Self cure acrylics were once used intra-orally. A catalyst and base material are mixed together, placed in the cavity prep and left to cure.
The Catalyst. Acrylic resins are thick pastes that harden via polymerization of the chemical constituents. Polymerization (hardening) is initiated by a catalyst -- heat is a catalyst. A self cure acrylic, requires a separate chemical catalyst for hardening/polymerization.
One requires heat. Self cure acrylic resins are materials that will set and cure without the need for additional heating of the material. Heat cured resins require additional steps to warm or heat the material in order for the acrylic resin to set or cure.