Estoppel is indeed defined as a "rule of evidence whereby one party is prevented from denying a previous assertion" (by Webster). This means that it may be used as a defence in a law suit, but not a cause of action.

"Simple" or "legal" estoppel is a legal doctrine here, unrelated to quasi-contract.

Promissory estoppel is an equitable doctrine, developed by Lord Denning in the early days of his career when he was Denning J. It operates to prevent the plaintiff from enforcing contractual rights where he has given the defendant reason to believe that they would not be enforced. This may be (or have been) stopped at any time by clearly announcing to the other party that the contract will now be held to in full.

This applies in England and Wales to promissory estoppel and legal estoppel, but not to proprietary estoppel, an equitable doctrine related to the constructive trust.