The term "laws" refers to all laws passed by the Legislature, which are subsequently bound in the Session Laws of that year. Statutes are a codification of the general and permanent laws, which are compiled and published every year as Minnesota Statutes or its supplement. By being codified into Minnesota Statutes, the laws are placed into the context of statutes that have been on the books in previous years.
Sometimes, it is difficult to understand a law unless it is placed into the proper context in Minnesota Statutes. But remember that not all laws will become statutes. Some laws, such as ones passed for a specific town or city, and appropriation measures, aren't included in Minnesota Statutes. So you won't find the appropriations made by the 2023 Legislature in the same set of books that contain the Minnesota statutes prohibiting drunk driving. The appropriation bills are probably the best examples of laws that aren't statutes.
Why are some laws not included in statutes? The main reason is that appropriation laws are applicable for only two years, whereas laws included in the statutes are intended to be permanent. And because local laws do not apply on a general level, they are not included in the statutes.
Administrative rules are promulgated in a very different manner than laws. Rules are created by executive branch state agencies and not by the legislature. However, executive branch state agencies only have the authority to adopt administrative rules when granted that authority by the legislature. The purpose of rules is to "implement or make specific the law enforced or administered by that agency or... govern its organization or procedure" (Minn. Stat. 14.02, subd. 4). Though laws and rules are distinct, and the process by which they come about is distinct, once rules are adopted they have the force and effect of law.
State agencies must follow a strict process when adopting rules. The rulemaking process is explained in detail in the Minnesota Administrative Procedure Act and in Rulemaking in Minnesota: A Guide, published by the Office of the Revisor of Statutes.