Three words with different meanings for different persons or companies!
Compatibility Personality Similarity
Sometimes the word compatibility means a high degree of similarity between several variables (religion, education, income, personality, likes and dislikes, etc.) of prospective mates; sometimes compatibility means a mix of similarity and complementarity between variables; sometimes when a dating site says compatibility or even chemistry, nobody really knows exactly what it means!
Some online dating sites offering compatibility matching methods use the word similarity as: "a proprietary Dyadic Adjustment Scale", others mean: "a proprietary multivariate linear regression equation", some say a mix of similarity and complementarity meaning: "a proprietary multivariate logistic regression equation", still others mix similarity and complementarity meaning: "a proprietary equation to calculate compatibility between prospective mates!"
Personality could be assessed by different methods.
No actual online dating site offering compatibility matching methods uses the 16PF5 normative test available in different languages, the 5th version actualized after Census 2000.