The DMA (Direct Market Access) has mainly been used in the Equities and Futures market to imply that the access to the market is via an exchange.
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The term DMA has been thrown around loosely in the Forex market as a trend of mislabeling or misusing the terms ECN and STP have left brokers looking for a new term to suggest or ultimately show their superior cleanliness at execution.
DMA implies that all trades are executed on exchange and your trades will affect the market. There is no interference between brokers or any dealing and market makers.