There is no universally accepted list of "three distinctions that underlie social science" among social scientists. The only place I've seen that specific phrase used is in the context of course materials about criminal justice research (see link below). There, it is used in the context of discussing the different forms that social science research can take. I'll frame my answer with that in mind, but what I say applies to social science in general.
1. Nomothetic versus idiographic explanation
One distinction that underlies different types of research concerns explanation. Some research is aimed at explaining a general category of phenomena. The goal is to make generalizations that apply to a wide range of cases -- to uncover general principles or laws. This is called nomothetic explanation. An example would be attempting to explain how early childhood stress contributes to the development of poor self-regulation skills. The researcher looks for an explanation that applies to a whole class of cases (e.g., children growing up in poverty in the United States). Nobody expects the single factor (childhood stress) to explain entirely why any specific individual develops poor regulation skills. Rather, researchers are looking for a general pattern that tends to hold across a wide range of individuals.
By contrast, idiographic explanations are aimed at understanding unique causal pathways and contingencies. They are concerned with individual cases.
For instance, how did a particular child, George, end up with poor self-regulation skills? Researchers aren't looking for answers that apply to all children, or even all kids in a certain category. They want to know what unique combination of circumstances and factors led him to develop the way he did. Research with this sort of explanation as a goal often takes the form of in-depth case studies.
2. Types of reasoning used: Inductive and deductive
Some social scientists like to talk as if inductive and deductive reasoning are inverse operations. You might read about inductive being "bottom up" reasoning and deductive being "top down" reasoning. The idea is that inductive reasoning starts by looking an individual case, the details of the data, and then making guesses or inferences about patterns and causation. You go from the specific to the general. Then "deductive reasoning" is presented as being the opposite of this, because you start with a generalization you take to be true, and then determine what specific conclusions necessarily follow from it.
The problem with this characterization is that it misses what "deductive" and "inductive" really means according to the formal study of logic and the philosophy of science. What's crucial isn't "top down" versus "bottom up," but reasoning that involves reaching conclusions that follow with logical certainty versus reasoning that involves conclusions that are merely probable. Reasoning from a syllogism like "All animals have DNA; humans are animals; therefore, all humans have DNA" is deductive. If the premises are true, then the conclusion must be true. With inductive reasoning, you don't have the conclusion nailed down as logically true. It's just likely.
So all social scientists make regular use of inductive reasoning. It's what everyone uses all the time -- whenever we make inferences that aren't, strictly speaking, guaranteed to follow by virtue of logic. But having said that, you can make some distinctions between research that pays explicit attention to deductive reasoning, and research that sticks mostly to inductive reasoning. For instance, when social scientists engage in controlled hypothesis testing (like conducting experiments), they often make use of the principles of deductive reasoning. They may try to come up with predictions that follow necessarily from their hypotheses, and then set up conditions to test those predictions.
3. Types of data used - qualitative versus quantitative
Another important distinction is the type of data that social scientists collect. Quantitative data are more likely to be collected when using a more deductive, hypothesis-testing approach. Researchers using quantitative data start by defining exactly what they will measure and how they will measure it. The aim is to record information numerically or make observations that can be sorted into discrete classes (like yes/no categories). A quantitative approach to data might, for instance, measure a child's self-regulation skills in terms of how many minutes he or she managed to avoid eating a forbidden treat.
A lot can get lost when you measure only quantitative data, so some social science research emphasizes qualitative data instead. Qualitative is non-numerical; it's the descriptive information you might gather by interviewing people with open-ended questions, or observing them and recording your subjective impressions of what's going on. Case studies -- in-depth analyses of individuals -- often make use of qualitative data.
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