united-states
But what is the interaction between these two types of actions? Is a
breach of contract a type of negligence in addition to being a
separate cause of action in its own right?
There are several categories of private lawsuits, but the two most common kinds a lawsuits for breach of contract, and lawsuits that are for violation of common law (and sometimes statutory) duties that are not for breach of contract call "torts" (also sometimes called "civil wrongs").
Sometimes, but not always, you can bring both a breach of contract lawsuit and a negligence lawsuit, in the same case. At other times, you can only bring the breach of contract lawsuit.
A breach of contract lawsuit is not a type of negligence. Among other things, breach of contract liability is usually "strict" (i.e. was the contract breached or not) rather than requiring proof of negligence.
In Colorado, there is a doctrine called the "Economic Loss Rule" also adopted in many other U.S. states. A 50 state summary of the "Economic Loss Rule" can be found here.
This rule states that if a duty is solely created by a contract and a breach of that duty causes only economic harm, and this duty does not arise from any independent legal duty, then you may sue for breach of contract, but your tort claim for negligence is barred by the economic loss rule. See, e.g., S K Peightal Engineers, LTD v. Mid Valley Real Estate Sols. V, LLC, 342 P.3d 868 (Colo. 2015).
If a breach of a contractual duty causes bodily harm, then the economic loss rule does not apply. The validity of the negligence claim and the breach of contract claim are considered separately and both may survive for a jury to consider on the merits.
Figuring out if a tort claim in a lawsuit is based upon a duty arising under a contract and is barred, or if it is based upon an independent duty and is not barred, is a non-trivial inquiry. There is a lot of case law addressing this question.
The way that the economic loss rule is formulated in Colorado is one of several ways of stating it. Your mileage may vary in another U.S. state.