The texture of mesoporous FAU-Y (FAUmes) prepared by surfactant-templating in basic media is a subject of debate. It is proposed that mesoporous FAU-Y consists of: (1) ordered mesoporous zeolite networks formed by a surfactant-assisted zeolite rearrangement process involving local dissolution and reconstruction of the crystalline framework, and (2) ordered mesoporous amorphous phases as Al-MCM-41, which coexist with zeolite nanodomains obtained by a dissolution-reassembly process. By the present systematic study, performed with FAU-Y (Si/Al = 15) in the presence of octadecyltrimethylammonium bromide and 0 < NaOH/Si ratio < 0.25 at 115 °C for 20 h, we demonstrate that mesoporous FAU zeolites consist, in fact, of a complex family of materials with textural features strongly impacted by the experimental conditions. Two main families have been disclosed: (1) for 0.0625 < NaOH/Si < 0.10, FAUmes are ordered mesoporous materials with zeolite walls, which coexist with zeolite nanodomains (100–200 nm) and (2) for 0.125 < NaOH/Si < 0.25, FAUmes are ordered mesoporous materials with amorphous walls as Al-MCM-41, which coexist with zeolite nanodomains (5–100 nm). The zeolite nanodomains decrease in size with the increase of NaOH/Si ratio. Increasing NaOH/Si ratio leads to an increase of mesopore volume, while the total surface area remains constant, and to a decrease of strong acidity in line with the decrease of micropore volume. The ordered mesoporous materials with zeolite walls feature the highest acidity strength. The ordered mesoporous materials with amorphous walls present additional large pores (50–200 nm), which increase in size and amount with the increase of NaOH/Si ratio. This alkaline treatment of FAU-Y represents a way to obtain ordered mesoporous materials with zeolite walls with high mesopore volume for NaOH/Si = 0.10 and a new way to synthesize mesoporous Al-MCM-41 materials containing extralarge pores (50–200 nm) ideal for optimal diffusion (NaOH/Si = 0.25).