Offshore brokers refer to brokers who are established in countries other than your country of residence. Most commonly, it is referred to brokers who are located in areas away from mainlands such as in islands and other small, secluded countries. Saint Vincent and Grenadines is one of the popular places for offshore brokers to build their companies.
In theory, they are just like any other broker. They provide their services by acting as a middleman between you and the financial asset you wish you trade with. They offer you their services for a certain amount of spread or commission which varies by the asset being traded. However, with rewards also comes a reasonable amount of risk.
Unlike fly-by-night brokers and pyramid schemes, bucket shops do have functioning trading activities, albeit for malicious intents.
Bucketing itself refers to practices by which brokers illegally generate profits from their clients' trades, such as frequent price misquotes or re-quotes,s in order executions, etc.
For example, a trader executes a buy position of EUR/USD at 0.8294. The broker confirms the transaction has been made while the truth is the order will be executed later when the price is at 0.8298.
The difference of 4 pips is kept by the broker as their own profit; a fact that will never be revealed to the trader.
The majority of forex brokers are hybrids that provide market maker, STP, and ECN conditions all at once. Even if brokers implement the STP/ECN model, their liquidity providers are still market makers.
Thus, it is not wrong to say that all forex brokers are basically "market makers". Therefore, based on this label, we cannot determine a broker's quality.