Suppose someone is trying to estimate the diagnostic prevalence of ADHD in a cohort of individuals born in 1985. What type of study is this? This is not a prospective cohort study because we are not comparing two groups (i.e an exposed and unexposed group). All individuals in this study are exposed (born in 1985).
It sounds like a cross-sectional study: it's a descriptive study, only looking at one specific time point.
That said, it could still be part of a prospective cohort study if the individuals in the 1985 birth cohort have been followed up over time. In that case, it would be cross-sectional study nested in a cohort study.
From the information you give, it could be several different study types. If the prevalence of ADHD is collected at a single time point, then this is a cross-sectional study, restricted to the population of individuals born in 1985. If the prevalence is collected over time, then this could be considered a cohort study. If the diagnoses were recorded for research purposes over time starting some time in the past, then this could be a prospective cohort. If you are now going back to medical records to ascertain diagnoses made in the past, then this is a retrospective cohort study.
You don't need to have exposed and unexposed groups to do a cohort study, but you do need to have a follow-up time component. Obviously to look at the effect of exposure on outcome you do need exposed and unexposed. As described above, this is a closed cohort (no one else can ever be born in 1985). You could compare the prevalence in this cohort to that in a cohort of, say, individuals born in 1995, or to the whole population currently. Or you could look within the birth cohort to assess the effects of other exposures, say, birth weight, on ADHD diagnosis.