With DMA (Direct Market Execution) execution forex traders are able to place orders directly with liquidity providers such as banks, other brokers, etc.
DMA brokers are the ones who can be called NDD (no-dealing desk) forex brokers.
ECN brokers are the ones who always provide Direct Market Access. But with an STP broker it does not mean you get DMA.
With DMA you get variable spreads and market execution when you get the best quote from one of the liquidity provider through the connection provided by your broker.
With DMA broker you always get STP (Straight Through Processing) that’s why they are referred to as DMA/STP brokers.
STP brokers have Instant Execution and will fill your orders on their side and only then will STP brokers pass your orders to their liquidity providers for hedging. That’s why you can often see re-quotes during the times the broker cannot find a profitable trading opportunity when you send your trading request.
DMA/STP brokers using Market Execution will route your orders to their liquidity providers directly and will them at the best rate offered by these liquidity providers. That’s why there are no re-quotes with DMA/STP brokers.
Take a note, that ECN/STP brokers are always Direct Market Access (DMA) as well.
Comparing DMA/STP and ECN/STP brokers one can say that both types have variable spreads. ECN/STP brokers get their compensation in the form of a commission. DMA/STP brokers are compensated with some fixed mark-up they have a contract for with each liquidity provider that is added to the bid/ask price.