Put simply.....Machine Edition (ME) is intended as an operator interface. Usually to allow an operator to monitor a single piece of equipment. It typically talks with just one Rockwell PLC system. Though it can talk with more than one, and with other vendor PLCs using OPC.
Typically this is used with Rockwell's PanelView Plus family of HMI touchscreen terminals. It is possible to run the software on a Windows PC without the PanelView hardware. But this is not typical.
Site Edition on the other hand is software typically used to monitor an entire process or facility. It can gather and store data, potentially from dozens of PLCs throughout a facility. It can use OPC to talk to nearly any brand of PLC system though it is geared to work best with Rockwell equipment.
Site Edition can run on a single PC or it can be distributed among multiple servers for performance and redundancy. Multiple users can use standard Windows PCs to connect and interact with the system.So ME usually displays information and lets an operator control a single piece of equipment, where SE can do the same for the entire facility. You might see SE in a control room where we can monitor the entire plant. ME would be used by the operator running a specific piece of equipment.
Although the software used for these two applications is the same, there are differences. The ME system is much more limited than SE.
I won't get into my opinions or competing products since that is not the question you asked. But be prepared, there are a lot of opinions here!
OG