Usually ero means a difference, distinction or a divorce.
- Mitä eroa on sanoilla tai ja vai? - What's the difference between tai and vai?
- Etsi viisi eroa. - Find five differences.
- Haluan eron. - I want a divorce.
Erota is to divorce or to separate.
(Here's an informative link about divorcing in Finland, and here's a song that you can sing to your ex in a Finnish karaoke.)
Erottaa is for example to fire and to tell apart.
- Kukaan ei voi erottaa meitä! - Nobody can separate/fire us!
- Mä en osaa erottaa niitä toisistaan. - I cannot tell the difference between them.
- A post about resigning and getting fired in Finnish
If you are confused by the similarity of these two verbs, you might enjoy my post about transitive and intransitive verbs.