Follow along with visualizations

       Error   Absolute Error  Squared Error
      --------------------------------------
Sum  | SE      S|E|            SE^2             
Mean | ME      M|E|            ME^S

Note: SE and ME don't work as distance metrics if you have errors with mixed signs as they will cancel out. Squares and absolute values don't suffer from this issue.

More commonly you'll see these abbreviations

       Error   Absolute Error  Squared Error
      --------------------------------------
Sum  | SE      SAE             SSE             
Mean | ME      MAE             MSE

Sometimes a square root is taken of the above metrics

RSE   - Root of Sum of Errors             - Not used
RME   - Root of Mean of Errors            - Not used
RSAE  - Root of Sum of Absolute Errors    - Uncommon
RMAE  - Root of Mean of Absolute Errors   - Uncommon
RSSE  - Root of Sum of Squared Errors     - Very common - This is the Euclidean Distance
RMSE  - Root of Mean of Squared Errors    - Common