Earlier quoted context omitted.
> Why in God’s name would you list them both? It’s a resume not a deposition. In the US resume fraud is a thing. Some companies like telecoms selectively check resumes for accuracy. Resume fraud can be a fireable offense.
If you lie about having a job this can be found out (they can call the place) If you omit one or several jobs, I don't know how they would know (call all places to see if you also worked there?).
It can be tracked during your background check (using SSN). They will make you sign a form that you authorize them to perform such a check. Fail to sign the form - job offer is rescinded. Again, depends on employer.