Two basic measures of association that you should be familiar with are relative risk (or risk ratio) and odds ratio. You should be able to both calculate and interpret them.
Risk refers to the probability of an event occurring over a certain period of time. Therefore, it typically implies a prospective study design. In Question #1, diabetic patients are followed over 5 years to assess for the development of acute coronary syndrome; that means it is possible to calculate and report 5-year risk of acute coronary events in these patients. Moreover, we can compare the 5-year risk of developing acute coronary syndrome in patients with a high baseline fibrinogen level (exposure group) to the patients with a normal baseline fibrinogen level (non-exposure group).
In case-control studies (like the one described in Question #2) patients are not followed over time to determine their outcome. Rather, the outcome (babies with neural tube defect) is known from the start of the study. Therefore it is impossible to calculate risk in such studies, but it is possible to inquire about past exposures. In case-control studies, we calculate the odds of exposure (the chance of being exposed to a particular factor) in case patients (those with disease) and compare it with the odds of exposure in control patients (those without disease). For example, in Question #2 we can calculate the odds of acetaminophen use in mothers having babies with a neural tube defect (cases) to mother having normal babies (controls).
In summary, relative risk compares the probability of developing an outcome between two groups over a certain period of time. It implies a prospective study design because the patients are followed over time to see whether or not they develop an outcome. Odds ratio compares the chance of exposure to a particular risk factor in cases and controls. Since risk can not be calculated directly in case-control studies (because they are not prospective), odds ratio is the measure of association used for this study design. Relative risk answers the question: within certain period of time, how many times are exposed people more likely to develop a particular event compared to unexposed people? Odds ratio answers the questions: how many times are diseased people more likely to be exposed to a particular factor compared to non-diseased people? Both relative risk and odds ratio are measured on a scale from 0 to infinity. The value of 1.0 indicates no difference between the two groups being compared. Odds ratio approximates relative risk when the disease under study is rare (so called 'rare disease assumption').