What is the symbol for a Fan on a circuit? Is it just Motor?
From an electronic device schematic point of view, a fan simplifies thus:

Fan ==> Motor ==> Inductor coil(s) 

Of course there are fans that do not use coils at all (piezo fans, coil-less motors), but let us set that aside for a moment. 

At the lowest level of abstraction, thus, a purely electrical schematic symbol using one or more inductors could suffice to indicate a motor, such as these symbols for DC motors:


(Source)

Another source suggests the stepper motor symbols below:
 ()



At a higher level of abstraction, the familiar symbol(s) with the letter "M" in a circular enclosure are commonplace, such as the brushless and brushed motor symbols illustrated in the question.

At a more pedantic level, some schematics use the M-circle symbol with a variety of enhancements to specify the various types of motors. This page provides an entire flood of symbols for specific motors.

 

Note the use of both inductor and M-circle to address both electrical and functional symbolization in the 3-phase series motor above.



Even so, our symbols so far do not indicate the use of the motor for a fan. For fans specifically, there isn't any universally followed symbol AFAIK, but a few variants show up in various documents:

 (clearly, a fan!)

 (AC motor -> fan)

The "Other standards" fan symbols shown in the question are not so common in electronic design related schematics, they are used typically for process engineering and electrical wiring. 



In summary, for lack of any universal standard, the symbol to be used is best determined by the purpose of the schematic: Is it important to account for inductive behavior, or to illustrate the type of motor, or at the most mundane and abstracted level, is it crucial to convey clearly that "This motor here is a fan"?