"Commercial use" in cases like this is actually just a shorthand to indicate that the product is dual-licensed under both an open source and a traditional paid-for commercial license.
Any "true" open source license will not discriminate against commercial use. (See clause 6 of the Open Source Definition.) However, open source licenses like the GPL contain clauses that are incompatible with most companies' approach to commercial software (since the GPL requires that you make your source code available if you incorporate GPL'ed code into your product).
Duel-licensing is a way to accommodate this and also provides a revenue stream for the company providing the software. For users that don't mind the restrictions of the GPL and don't need support, the product is available under an open source license. For users for whom the GPL's restrictions would be incompatible with their business model, and for users that do need support, a commercial license is available.
You gave the specific example of the Screwturn wiki, which is dual-licensed under the GPL and a commercial license. Under the terms of the GPL (i.e., without getting a "commercial" license), you can do the following:
In other words, there's a lot that you can do without getting a commercial license. This is especially true for web-based software, since people can use web-based software without it being distributed to them. Screwturn's web site even acknowledges this: they state that the commercial license is for "either integrating it in a commercial application, or using it in an enterprise environment where free software is not allowed," not for any use related to commerce.
All of the preceding is merely my understanding and is not intended to be legal advice. Consult your lawyer to be certain.