I've been invited for a chat for a potential PhD position by a professor I'm interested in working with. He also wants me to give a short presentation on some experiments I've done in the past that I'm proud of. What am I supposed to expect from this? Is it going to be a real interview? My master's dissertation has essentially been on a similar field of study. Am I supposed to explain everything from the basics in the presentation or just talk about the experiments that he asked for and assume the professor knows/understands stuff? What am I going to be judged on? What are the right questions for me to ask?
If I were the professor, I'd prefer to chat with you, rather than do some formal thing. If I'm looking for a student, I want to put them in the least stressful situation possible, because I'm more interested in him/her when they are at their best. In my lab, I don't like useless stress. Creativity manifests itself in stressful situations, but the coolest stuff happens when people aren't afraid and are driven by the passion for exploration. There is enough time in a PhD life to be put on the spot, and you can be trained for that to a great extent.
Slides are a great aid, and will be helpful in explaining your research. There is probably a lot of stuff a prospective PhD candidate doesn't know about and is unsure of, and a formal interview is great at revealing it, but is not so great at revealing what the candidate does know.
I remember my best student, how nervous was when we met first. I think I underestimated him then because he simply couldn't talk about his research work freely. Two years later I understood how good he really was, and three years later, had his own publications. Now he is better than I ever was.
I also want to add that the "chat" might mean that is up to you if you feel comfortable giving a talk in front of more people than the potential advisor.
Yes, this is an interview. Or at least a part of an interview - depending on your location, there may be a more formal one later. As a rule of thumb, both for academia and industry, whenever you meet with a prospective employer, be it for a coffee or lunch, a "chat" or something else, it is part of the interview.
As for the chat itself. If he asked you to give a short presentation, you should prepare to give a rather thorough one; ie. be prepared to explain basic stuff as well. If you have no idea about the format (time, place, equipment, audience (eg. is it just him?)), ask him. In my field it would be common to prepare some slides for such a presentation, but for others you would do without. It is always nice to know roughly how long time you have when preparing. Important: If the prof. says that you have, say, 20 minutes, then prepare to stick to that.
You can ask about details of the research, what is expected of PhD students wrt. teaching, possibilities for traveling and other things you are curious about.
Yes this is very much an interview, although you might find it less formal than some because in many ways a PhD supervisor really wants to know whether the two of you can work effectively together. Take it seriously, be friendly and professional - don't try to do everything in the presentation (concise and clever, not over-burdened with detail or obscure). Make an impression of enthusiasm and willingness to throw yourself into the project, even if you don't quite know where it will go. But show that you've thought at least about potential timelines and plans.
If it was just a chat, I would say it's more like a get to know you. He would want to see how you present yourself, make sure you aren't crazy, not an arrogant person, etc. But because he wants to see you present some of your work, I would absolutely treat it like an interview.
If I was him, I would say "Chat" just to keep things informal, casual, and keep the pressure off both you and him. There's lots of reasons he might not want to start a formal process like an official interview, but sounds like you are in a good position. I wouldn't over dress, but look nice. Create a PowerPoint with 4 or 5 slides for each experiment you want to talk about. Prepare for the normal interview questions, and STAR questions.