Type refers to the way the dishwasher is built into the cabinet.
Freestanding, with a worktop – can generally be built-in as well because the worktop can be removed.
Built-in – might not have top or side panels; must be enclosed and anchored to prevent it from tipping forward when fully loaded and dish racks are pulled out.
Semi-integrated – a built-in type that allows you to fit a panel to the door under the control fascia to match the rest of your kitchen cupboard doors.
Fully integrated – built-in with the whole front matching your kitchen and the controls inside the door.
Compact – refers to the height. These tend to be built in (like an oven) or benchtop dishwashers.
Slimline – a full height dishwasher, but they tend to be a good deal narrower to suit narrow margin installs.