I am confused between these two types of forces, what makes them different? For example, a moving ferromagnetic object in a solenoid that moves because of a magnetic field created. Which field would be applied here?
The complete mathematical description of the electromagnetic field contains portions that are magnetic and portions which are electrostatic. Isolated cases of purely magnetic and electrostatic fields that are standing still or otherwise not changing in time are common. But when motion or change in field strength is involved, these two types of fields become intermingled and both fields must be included to describe what's going on. I am not clear what you are asking in the second part of your question.