A scatter plot templates page like this one is really answering one question: does one measure move with another? Every chart in this family puts a dot for each row of data on two axes (one variable across the bottom, one up the side) and lets you read the relationship at a glance. Height against weight, ad spend against sign-ups, temperature against ice cream sales. If the dots trend upward together you've got a positive relationship; if one goes up as the other goes down, negative; if they're scattered with no pattern, there's probably nothing there worth reporting.
The three templates differ in how much they add to that basic x-y plot. A plain scatter plot handles two variables and stops there: the cleanest option when you just need to show the relationship itself. Add a third variable as dot size with a bubble chart, so you can show, say, GDP against life expectancy with population as the bubble radius, without needing a third axis. A quadrant chart takes the same two-variable layout and drops in a horizontal and vertical reference line (often the average of each axis), splitting the plot into four labeled regions, which is the shape you want when the point isn't the raw correlation but which category each item falls into (high-growth/low-share vs. low-growth/high-share, and so on).
One honest caveat worth stating up front: a scatter plot shows correlation, not causation. Two variables can trend together because one causes the other, because both are driven by a third factor, or by coincidence in a small dataset. PlotSet won't tell you which of those it is. That's still a judgment call for whoever's reading the chart, and a page that pretends otherwise is doing its readers a disservice.