不要 + verb forbids the listener's action (不要去 — don't go); plain 不 + verb only states a will is absent (不去 — I won't go). One halts another's deed, the other declines your own.
object after 不要 for a command: 不要話 → 不要說話(不要 bars a verb, not a noun)
negating your own plan as a command: 我不要去 (I refuse to go) used to mean 'I won't go' → 我不去
請 placed after 不要: 不要請說話 → 請不要說話(請 bows in front of the whole command)
English 'don't' is one word for every register; learners pick 不要 where the casual 別 fits, or read 不要 as 'don't want' instead of a command to the listener.