scatter draws points without lines connecting them whereas plot may or may not plot the lines, depending on the arguments.
scatter returns a handle to an object called scattergroup whereas plot returns a handle to an object called lineseries. The scattergroup object has some properties (for example, for associating the size of the dots to a variable in the workspace) that are not present in the lineseries objects. Analogously, the lineseries has some properties (for exmaple, for controlling the type of lines) that are not present in the scattergroup object.
scatter allows you to specify a different colour and a different size for each point individually. It is not possible to do that with plot.
Hope this helps.