Heterotypical continuity means that an underlying (developmental) process or impairment stays the same, but the manifestations do not stay the same. For example a child with autism might first show impairments of non-verbal skills and problems in eye-contact. In a later developmental stage the manifestations would be different, such as stereotypical behaviour or language problems.
In psychopathological progression one disorder can be seen as a risk factor for developing another disorder. For example eating disorders such as anorexia nervosa have a influence on neurotransmitter levels such as serotonin. Imbalance of that neurotransmitter is related to general anxiety disorder and depression. In that way eating disorder do not cause depression, but it certainly puts the individual at a higher risk.
Whereas comorbidity is a correlational construct, the concepts of heterotypic continuity and psychopathological progression are causal theories in a developmental framework, that take the development of the individual into account. One could argue that, where comorbidity uses data to state a fact, the other two concepts actually try to explain the process.
Homeotypic continuity can be seen as the opposite of heterotypic continuity. Whereas in heterotypic continuity the process stays the same and the manifestations change, in homeotypic continuity the manifestations stay the same, but the underlying process changes. For example a child might resort to aggression, because it lacks the necessary skills to make contact with peers at schools. Later in life aggression against peers might be mainly attributed to an antisocial personal disorder.