规矩- refer to custom of a certain group like family,school, religion, or even some underworld rules. Can be right, but mostly not, or just be constraints for daily behaviors. 规律- the periodic facts in nature or human society, like the it's going cold in winter or bears have hibernation. 规则- codes for games or works.usually authorized by professionals

Hi. I would use some examples to illustrate the uses of these words: "你到了我们家里，就得守咱家的规矩" （人为制定的） “比赛的规矩” （人为制定的） “学校了的规矩” （人为制定的） “部队里的规矩” （人为制定的） "规矩" and "规则" are the same meaning-wise, but "规矩" is more of an oral rule or common practice, which is not formal or official and is less binding, while "规则" implies the rule or the common practices are formally written in a document, which is more binding. "规律" 指的是客观的自然或社会的rule，不受人为意志影响的不可改变的准则。 “规则/规矩”指的是人为制定的rule，受到人为意志的影响，可以被改变。

They're actually quite distinct. "规矩“ refers to conventions, norms. "规律" refers to patterns, regularities. ”规则" refers to codes, rules.