A shopping channel is generally live 24 hours a day, 7 days a week with a host or hosts selling items. For example, they may be selling a computer, or a piece of jewelry, or a lawn mower with an 800 number to call that channel to buy the item while it's being sold at the Special price.
The 800 number is for the shopping network's call center. The shopping channel generally backs the products they sell like any other store.
An infomercial is what is known as a "long-form commercial". These are generally 30 minute commercials disguised as a TV program, like a talk show, or documentary, selling a particular product or service. I recently heard the term "Documercial" which is a documentary about a topic which is used to sell you the product they are discussing. The company making the infomercial buys time on a local TV station or cable channel. The company making the infomercial generally does not own or is not affiliated with the channel the infomercial is aired on. The 800 number to buy the product is to an independent call center, not the channel. The channel usually airs a disclaimer at the beginning and end of the infomercial absolving itself of any liability should the person be dissatisfied with the product or service, and really has nothing to do with the company pushing the product or service other than they sold commercial time to that company.
Does that make sense?