In a continuous transect, you record vegetation along the whole length of the transect line.
This can be achieved by turning over a frame quadrat on the side perpendicular to the transect line as soon as you have finished recording at each point.
For a shorter distance, such as an investigation into how vegetation changes across a single dune slack, a continuous transect could be useful. But a typical 300m transect, perhaps sampled with a 1m2 quadrat, would require many more samples than you could realistically take.
In an interrupted transect, you only record vegetation at intervals along the transect line.
Quadrat sampling points (or 'stations') can be regularly spaced along the line (perhaps every 30m). Or you can choose to place stations at specific points of interest along the transect line.
Generally one quadrat per station is not enough. Instead take at least 3-5 quadrat readings at each station. You could do this by placing a frame quadrats next to the transect line, then turning the quadrat over on its side to take the next quadrat reading.You will collect data across a broader belt; a technique known as an interrupted belt transect.