Response bias is a type of selection bias. It occurs when patients enroll themselves in a trial, which results in a non-representative sample. For example, the people who respond to a survey will frequently be different from those people who chose to ignore the survey. This is also known as volunteer bias. (Response bias generally refers to survey based research, whereas volunteer bias is used for other research methodologies.) Self-selection bias is another term that refers to this phenomenon.
Non-respondent bias refers to the same phenomenon, but is specifically referring to the fact that people who fail to respond to a survey may be systematically different from the rest of the population.
The term “response bias” is used differently by different people. Although I have frequently found it used as above, some people would actual claim this definition is incorrect. Sedwick (2014) defines response bias as the systematic difference between the way that respondents answer questions and the truth. For example, a survey respondent may claim that they never drink and drive, when in fact they have done so on occasion. This would make response bias a type of measurement bias rather than selection bias. (Sedgwick 2014)
Sedgwick P. Non-response bias versus response bias BMJ. 2014; 348:g2573-g2573.
Sackett DL. Bias in analytic research. Journal of chronic diseases. 1979; 32(1-2):51-63. PMID: 447779