An Open Day is a public event for anyone thinking of applying.
A Visit Day is by invitation only - and for only those applicants who have been made an offer by that Uni/Dept.
Visit Days are designed to help you make a decision re. your Firm/Insurance. So there will be a general tour of the Dept, opportunities to talk to current students (they usually lead the tours), a group chat from the Admissions Tutor(s) and usually a one-to-one chat with an academic. They aren't interviews so don't get worried - its all designed to tell you what Bristol could offer you. You've already got an offer - they like you! So don't panic about the one-to-one - it really is just a 'chat', not a formal interview. Bring a parent is fine, but lots of people come on their own. And the Visit Days are usually topped off with a bus trip around Bristol - just to show you what a great place it is.
PS> These sort of visits are a great way to practise 'talking to new people' - when you are in a queue to get into a room, or sitting next to another applicant, just talk to them - 'My name is .... I'm from ..... What about you?' These could be the people you will be spending the next 3 years with, and these sort of encounters will make you feel more at home and confident. Try it.