The terms you are confused about are: "domain objects", "domain entities" and "model objects". While usually used interchangeably, the domain entities and model object can also be instances of active record pattern (basically: domain objects with added storage logic).
In ordinary domain object there is no storage logic. It gets handled by data mappers.
The term "model objects" comes from Fowler's books (read PoEAA for more details), and, IMHO, is part of the confusions MVC, because the entire model is an application layer (MVC consists of it and presentation layer), which contains those "model objects", which are usually dealt with by services (in that image, the model layer is all three concentric circles together).
I much prefer to use "domain object" term instead.
The term "domain entity" (or "entity object") is usually used when author implies that the object is a direct representation of a storage structure (more often - a database table). These are also almost always implementations of active record.
P.S.: in some articles you would also see term "models" (plural). It usually is not directly related to MVC design pattern, because it talks about Rails-like architecture, where "models" are just active records, that get directly exposed-to/created-by controller.
.. not sure whether this confused you more