We must have the same expectations for students on a campus as we do online. We should hold our students to maintain excellence regardless of where they are. Cheating does happen. There is no guarantee that the student is posting their own discussions or taking their own tests. This type of anonymity makes it harder in some ways.
Tools such as Turnitin do help. However, the policies we have about such tools must come from the top down. Students will not tend to use these unless it is mandatory. It can only be mandatory if it is supported and expected from administration.
We know that cheating is the same because we understand it to be dishonest. The student knows it to be dishonest as well. Should we be concerned? Yes. A good example of this is plagiarism. This is a huge problem.
Students must first understand the importance and purpose of citing sources. APA standards are important for the classroom for several reasons. The obvious answer is to ensure that proper credit is given to the proper author. At the same time, the key word here is standards. It creates a formal way to write that everyone will understand. Just like medical terminology is essential for clearly understanding health sciences, this allows readers to navigate around the paper easily. There are certain expectations for any APA paper and these can easily be found with standards.
The point of this is that it is too easy to be lazy and then cheat in the classroom if expectations for excellence are not given from the institution and the instructor.