What is the difference between two variables being proportional versus being directly proportional?

I hear these expressions being thrown around, and realize that "proportional" may also incorporate inverse proportion, but are there any other differences?

Besides considering whether the two variables may be in inverse proportion, when two variables $x$ and $y$ are "proportional," you may also need to consider the difference between cases like:

$$x = ky$$

and

$$x = ky^2$$

where $k$ is the constant of proportion.

But here "directly proportional" can also be used if the writer is clear about the relationship between the variables. For example, in the 2nd case, the writer could write:

"$x$ is directional proportional to $y^2$"

Hope that helps.

Nothing really. When all other information is omitted its safe to assume that proportional means directly proportional. It is just an assumption, granted, but its not an unreasonable one since any other type of proportion would have been specified.