Denver Public Schools has several "contract" schools that are not charter schools. In fact, a couple of the contract schools are private schools with only certain grade levels operating under a contract with DPS. The recently closed Challenges, Choices and Images Charter Schools is now operating under a contract and isn't a charter school for the remainder of this school year.
What's the difference? Very little. "Charter" and "contract" are synonymous. Charter schools can get waiver from state statute, rules and district regulations much easier than a contract school can. Although the legislation that passed last session authorizing "innovation" schools makes that easier, too.
Generally, a contract school has a closer tie with the district and doesn't have contractual autonomy guaranteed by the Charter Schools Act. However, provisions in the contract may allow for a great deal of autonomy, even autonomy in employing at-will employees.
This is another gray area of the law. I've read contracts with "contract" schools that provide for greater flexibility and autonomy than a charter schools. The provisions in each contract or charter are unique and may vary greatly.
Technically, a charter school operates via a contract with an authorizers, has waivers (or the ability to request waivers) and autonomy as provided in the state Charter Schools Act. Contract schools are unique according to each district that operates them. In fact, they may even be called different titles, such as "magnet," "option," or "focus." These schools may not even have a contract: it's totally up to the district in which they operate.
Some schools such as D'Evelyn Junior/Senior High, are commonly mistakenly called a charter school. D'Evelyn is an option school in Jefferson County. It originally applied for a charter and option status simultaneously in 1994, but ultimately chose the option route. Challenges, Choices and Images closed and is now operating as Amandla Academy as a contract school with DPS. It will probably operate as a charter school next year, however.
Even though schools may "look" like a charter school, that doesn't mean they are. Each school is unique and the key to "what" they are is understood by reading the contract/charter.