In motion satellite dome 101 by me.
Domes can see one, and only one, satellite at a time and only in one band (At this time) however SOME domes (Need make and model to know) Can switch between 2 or 3 different "Brids" (Short for Satellite) at a time.
DirecTV: (Different from DirecHDTV) uses one bird for most all customers 101W, south of, roughly Kansas, it can be seen from most anywhere in the 48.
DirecHDTV will not work with a dome,, only SD,, though some receivers will work, but not for HD programming or channels. This is because the HD channels are in a different frequency band and the antenna can not tune them.
Dish, uses 2 (SD) And 3 (HD) and since they are closer to Hawaii than kansas they have a 2nd arc over the Atlantic for folks in Myrtle beach (on the east coast) All can be seen by the dome
SOME domes, the controller will respond to the receiver's request to change birds, some do not,, again we need the make and model Some require programming or updates as well.
Finally: Single or dual? What does it mean, and can domes do that?
Single means ONE output, ONE sat and either ODD or EVEN transponders but not both at once. Has nothign to do with the number of birds it can see at one time.
DUAL likewise has nothing to do with number of birds but means it has TWO outputs and can see both odd and even transponders at the same time, More on this later.
With DirecTV, a DUAL can provide signal to 2 or more (with proper switch) receivers or a multi-channel DVR..
With DISH, You really should have multiple domes to do that since the odds are sooner or later the two receivers or DVR channels will want different birds and someone will be... unhappy.
Odd/Even transponders.... In order to double the badwidth Satellite TV uses each frequency twice.. By means of something called circular polarization they sent TWO signals in the frequency bandwidth normally taken by one. One is right hand and one is left hand.
The ground antenna can separate them very easily. I will explain how.
Imagine a turn buckle, This is a device that consists of two bolts, One righ hand one left hand thread,, Usually eye bolts, and a "Bridge" style nut that joins them together, one end is right hand one is left hand.
This way when you tighten both bolts pull in.
Now, if you tried to put the bolts in the wrong end.. Would not work, won't thread in. Radio waves act like the threads on the bolt, if they are "Twisted" the wrong way they do not go in. That easy.