How you define sample selection depends largely on the study. As long as you use a probabilistic sampling method, no method is better than another in absolute terms. Methodology cannot stand alone, without a scientific rationale no research methodology will ever make sense.

In a cross-sectional study, time doesn't matter: but how you define groups depends on the kind of comparisons you're interested in.

In a prospective cohort you enrol subjects depending on their exposition and you follow-up them during a certain period of time to see who develops the outcome of interest. Please note that the fact you follow your subjects over time means that you usually expect a higher rate of drop outs and/or withdrawals than in a cross-sectional study.

I believe in cross sectional study, the research starts with participants whose disease and exposure statuses are unknown. Strictly speaking, you don't select cases and controls but rather study participants whose disease and exposure statuses will be ascertained at the same time. From a theoritical point of view in a prospective cohort study participants are selected in the study based on their exposure status (exposed and not exposed) and the absence of the disease in all of them (they must all be at risk of developping the disease) at the time of inclusion into follow up.

Common disorder population with an additional risk factor will be cases while those with out risk factor will be considered as controls. e.g if a researcher goes to evaluate control of lipid abnormalities in a population of IHD with and with out H.Pylori. IHD patients -ve for h.pylori will be controls while +ve H. pylori will be case ,both can be compared in a cross sectional study.

There is no comparison group in cross-sectional study and it is not prospective