Order of application of Modifiers, object level

Order of modifiers is important on object basis, but it can also be important on an object-by-object basis. EG, if you have a subdivided Object that is intended to adhere closely to another, different subdivided Object, it’s best if the first object is subdivided FIRST, prior to the 2nd object being shrinkwrapped to it.

  1. Is this under the users’ control?
  2. If not, what is the order that Blender follows by default? (For instance, in C4D there is a strict order than includes something like the order they are in the Object Manager, rather like the conventional order in a math equation.)

The default modifier stack works from top to bottom on individual objects and it’s not dependent on anything else. In your shrinkwrap example, you would add a subdivision surface modifier to the first and second objects individually, and then add a shrinkwrap modifier to the second object.

Mostly not. Of course, within the object you’re actually editing you’re free to place modifiers as needed. But targeting other objects that have modifiers on them, you’re typically using the final modified version (taking into account which modifiers are enabled/disabled). There are a few instances where we do have some limited control as to whether take the base mesh or the final result (IIRC, in particle systems), but other than those, no, not under user’s control.