I have a general question about regression in Stata.
What is the main difference between commands:
rreg (Huber regression) and
What is the explanation for one and the other?
You are confusing quite different things, but the main reason for your confusion is that terminology in statistical science is indeed inconsistent here.
The Stata command
rreg implements one flavour of robust regression that is (in a very limited sense) robust to outliers in the data. What it does is well documented in the Stata manuals and also discussed elsewhere in this forum at
Quantile regression vs. Li's regression: which should I use, and when?. It remains visible as a matter of continuity but even among Stata programs it has (in my opinion) been superseded long since by alternatives. The thread just cited offers an independent and authoritative opinion in agreement.
The Stata option (not command)
robust implements robust (Huber-White-sandwich) standard errors that are offered as more honest standard errors in the face, principally, of heteroscedasticity. Asking for robust standard errors does not amount to robust regression in the sense just discussed, and outliers and long tails in any of the variables will have exactly the effect they have otherwise on coefficient estimates; the difference is that your standard errors may differ, affecting any quantities that depend on them.