Here's my little more complete response to someone who asked the same thing back in May:
"ppm is a dimensionless measure. That is, it is volume/volume or mass over mass or anything over that same thing. mg/L is obviously a mass/volume, fundamentally the two are different. However, for dilute concentrations of liquid water (or really dilute like Maj said) a ppm is a mg/L to the accuracy of anything we can commonly find in the house or the test equipement aquarists buy. If you are doing really detailed laboratory testing it would be inaccurate, but for fishkeeping, it is more than fine."