On the outlet of my dishwasher/disposal one of the receptacles is open hot. (I tested with a gfci tester). The disposal works in this receptacle. When I plug the disposal into the other receptacle the disposal starts running (without use of wall switch). Why does it start the disposal unit on this receptacle and not the other (open hot)? And why would open hot be used to connect outlet?
Open hot is expected if that outlet is controlled by a switch (while the switch is off), which is typical of garbage disposals.
You say that in one receptacle "the disposal works" and in the other "it starts running", so I will assume "works" means "is controlled by the switch as expected", and that your question is just why this is so.
Here's what this circuit typically looks like:
Note the white neutral wire is connected (by the "tab") to both top and bottom of the outlet. Also, for simplicity, this diagram doesn't show ground wires, or a neutral wire going to the switch (which is required since NEC 2011).
When the switch is open, there is no hot connected on the top outlet, hence the tester seeing 'open hot'. If you turn the switch on, you should see a normal working circuit (same on both top and bottom).