We often throw around terms like "statutory requirements", "regulatory requirements", and "contract requirements". Often times, these terms are used interchangeably and sometimes imprecisely.
The fundamental difference is that statutes are enacted by Congress and signed into law by the President whereas regulations are issued by executive agencies in order to implement statutes enacted by Congress. An example of a statute would be Public Law 87-653, The Truth in Negotiations Act. An example of a regulation would be FAR Part 31 Cost Principles. Regulations must be consistent with the enabling statute and the agency must follow the rule making process of the Administrative Procedures Act (i.e. publication of proposed regulation, public comment, final regulation). Regulations have the "force and effect of law" meaning they are just as enforceable as statutes.
From a practical matter then, it makes no difference to a Government contractor whether a requirement flows directly from a statute or whether it flows from a regulation implementing a statute. The contractor must comply either way.
"Contract Requirements" can be statutory, regulatory, or something else. Government contracts are full of regulatory and statutory requirements as well as requirements that are specific or unique to the particular contract. For example, a contract might require contractors to advise the contracting officer when making key personnel moves. Such a requirement has no basis in statute or regulation but is no less enforceable under the contract.