A One-way ANOVA has one IV with three or more levels
A Two-way ANOVA has twoIV's that each have two or more levels that are related, unrelated or mixed
A factorial ANOVA has three or more IV's that each have two or more levels
A MANOVA has one or more IV's that each have two or more levels and two or more DV's
Regression puts emphasis on how one variable affects the others. Multiple Linear Regression uses two or more independent variables to predict the outcome of a dependent variable