A method for making a semiconductor device may include forming, above a substrate, first and second semiconductor regions laterally adjacent one another and each including a first semiconductor material. The first semiconductor region may have a greater vertical thickness than the second semiconductor region and define a sidewall with the second semiconductor region. The method may further include forming a spacer above the second semiconductor region and adjacent the sidewall, and forming a third semiconductor region above the second semiconductor region and adjacent the spacer, with the second semiconductor region including a second semiconductor material different than the first semiconductor material. The method may also include removing the spacer and portions of the first semiconductor material beneath the spacer, forming a first set of fins from the first semiconductor region, and forming a second set of fins from the second and third semiconductor regions.