Finger-like protrusions in cells are mostly generated by an active actin cytoskeleton pushing against the cell membrane. Conventional filopodia, localized at the leading edge of the cells, are long and thin protrusions composed of parallel actin filaments that emanate from a branched actin network. In contrast, dendritic filopodia, precursors of dendritic spines in neurons, are entirely filled in with a branched actin network. Here, we investigate in vitro how the dynamics of branched actin structures, polymerized at a membrane surface, trigger the formation of both protrusion types. Using supported bilayers and liposomes, we show that a decrease in the amount of activation sites at the membrane surface leads to the appearance of heterogeneities in the actin network coverage. Such heterogeneities promote the formation of membrane protrusions, and the size of heterogeneity patches matches the one of the protrusion base. Protrusion shape, cylindrical or conical, directly correlates with the absence or the presence of actin branches, respectively.