Although these two concepts sound similar, they are used rather differently in political science.
Regime affinities are said to exist between states. When states have regimes that are likely to be friendly to one another, they are said to have regime affinity with one another. We might say that China and Vietnam have regime affinity because they are both nominall communist. Regime affinity can be negative as well, typically because of ideological differences, but also because of historical conflicts between two states. Thus, we can say that the US and Iran have negative regime affinity both because of different ideologies and because of a very negative historical relationship.
Regime preference is an individual-level phenomenon. People have regime preferences because they prefer one type of government to another. You will sometimes see regime preference polling done in various countries. In such polling, people are asked, for example, whether democracy is always the best system or authoritarianism is sometimes desirable. A person's attitudes on this kind of question constitute his or her regime preference.