Odds ratio (OR) and relative risk ratio (RR) are measures of an association between two binary variables.
In a cohort study an exposure may be associated with a later increased or decreased risk for a specific disease. In this case these associations are often labelled “risk odds ratio (ROR)” and “risk ratio (RR)”.
In cross-sectional studies where the prevalence of one binary variable is associated with the simultaneous prevalence of another binary variable the same measures are often labelled “prevalence odds ratio (POR)” and “prevalence ratio (PR)” (the latter is sometimes also referred to as “prevalence rate ratio”).
OR and ROR are mathematically the same. Similarily thes RR and PR are mathematically the same.
Relative risk is often considered a the better estimate of association, at least when the prevalence of any of the variables is above 10% . However, odds ratio is most often uses since most statistical software delivers odds ratios when doing logistic regression.
Ronny Gunnarsson. Relative risk / Odds ratio [in Science Network TV]. Available at: https://science-network.tv/relative-risk-odds-ratio/. Accessed July 21, 2019.