In math-speak, Econometrics is a subset of Statistics.
The difference being that Statistics covers a wider scope, and Econometrics only a small subsection.
Econometricians like to market themselves as being statisticians who use data that is sourced from real world data (e.g. macroeconomic indicators, stock prices, exchange rates, etc) where experiments cannot be performed (i.e. you can't change interest rates just to study its effect... you'll cause mayhem
![Stick Out Tongue :p :p](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
).
At the end of the day, Econometrics is for those who are moderate with Mathematics. If you're good at it, do a maths or stats degree.