Transition from PhD to project-manager position
If you've taken Project Management classes and have taken lead roles in regards to projects and BS and MS students, you'll find Project Management to be a more intense version of that. For example, you'll be needing to ensure everyone is working at the pace they should, getting the needed work done, and be prepared to figure out ways to remedy issues that occur. You will be working closely with stockholders, include managerial people, customers, etc, and you need to have the ability to answer any questions they may have regarding your project, even though you yourself are not the one directly creating that content. You'll need to figure out how to effectively communicate with people under you to get a sense of what they're doing and how things will impact the project. Be prepared to do scheduling of the project, which includes figuring out things in terms of Man Hours required for project in contrast to what you have available as resources. A lot of these things are similar in respect to what you've done in school, though to a higher degree: there's more riding on it, and these people aren't grading you, they're expecting it to be done right the first time.

As far as difficulties, if you have done all the above in classes or with your BS and MS students, then just be prepared for the faster pace and higher volume of stockholders. It can be a bit overwhelming, but doable.

Having a technical PhD will help you in these situations, because you'll have a better understanding of what your workers need to complete their tasks, how fast it will take them, and what it is exactly that you're working on. In fact, it will give you a leg up on other candidates or PMs that don't have technical backgrounds. If you can listen to a technical explanation of what's happening, and relay it to stockholders in a way that non-technical people can understand, you'll be fine.