Dear Sara,
Expansion growth happens when the "population growth rate" increases over time. In Logistic growth model, the population growth rate "decreases" over time, and in Exponential growth models, the population growth rate is "fixed" over time. In Constant size models, the population growth rate is "zero".
For more information, you can see the paper by Pybus and Rambaut (2002):
Pybus, O. G., and A. Rambaut. 2002. GENIE: estimating demographic history from molecular phylogenies. Bioinformatics 18:1404–1405.
Best,
Sana