In an accelerated longitudinal design, you have multiple cohorts that differ in their age at study onset. For example, each cohort is longitudinally followed over ten years and you have five cohorts that each start at age 20, 30, 40, 50, and 60, then you cover longitudinal changes over age range 20 to 70 (=60+10) but it takes only a total of 10 years for the study to complete. Of course, you now throw cohort differences in the mix, that is, people may not only differ because of their ages but also because they were born at different times. Depending on the accelerated design chosen, it may be possible to model the cohort differences. In particular, it makes sense to overlap the age ranges of the different cohorts, which allows us to estimate differences between different cohorts at same ages.
In my experience, researchers may often refer to single cohort longitudinal design just as longitudinal designs, but really longitudinal design is the umbrella term for every design that has multiple time points.