Unca Scrooge,
On a chart, the "period" of the moving average will be based on whatever the period of the chart is; so a daily chart will have daily moving averages (dma) weekly charts will have WMA, etc.
However the TYPE of moving average is what you're referring to. SMA=simple moving average, EMA = Exponential Moving average, WMA = Weighted Moving average.
So a simple moving average on a daily chart I suppose should really be called a DSMA so that you get BOTH "period" and "type" info in the abbreviation.
Usually the abbreviation refers to the TYPE (SMA, EMA, WMA), because the PERIOD is understood to be the period of whatever chart you're using.
On this board however, I think the term "dma" is used to point out that since we're often using the average as a support level, you don't want to be using a weekly one when you should be using a daily one or vice-versa, so the time frame becomes important in the discussion.