I found your quoted text in Section 5-4-6 of the AIM. You quote paragraphs b and c of the section. I will break down paragraphs a, b, and c using examples. Each paragraph is discussing a situation in which a pilot has been cleared to a holding fix (perhaps by clearance delivery, i.e. the last fix in the flight plan) and has been "cleared ... approach" prior to reaching that fix.
Paragraph 5-4-6 a
An aircraft which has been cleared to a holding fix and subsequently “cleared . . . approach” has not received new routing. Even though clearance for the approach may have been issued prior to the aircraft reaching the holding fix, ATC would expect the pilot to proceed via the holding fix (his/her last assigned route), and the feeder route associated with that fix (if a feeder route is published on the approach chart) to the initial approach fix (IAF) to commence the approach.
Summary: What to do when there is a feeder route from the holding fix to the IAF.
For example, prior to departure, a pilot calls clearance delivery and receives clearance to KMOB via V198 BROOKLEY VOR. They plan to shoot the ILS 15. Here is the approach plate and the chart.
Notice the feeder route from BROOKLEY to the IAF. If the pilot is "cleared ... approach" while on V198 transiting to BROOKLEY, their route has not changed. They must proceed to BROOKLEY as cleared, and then use the feeder from BROOKLEY to CAYAT (IAF). They may not turn directly to CAYAT unless specifically cleared to do so.
Paragraph 5-4-6 b
If a feeder route to an IAF begins at a fix located along the route of flight prior to reaching the holding fix, and clearance for an approach is issued, a pilot should commence the approach via the published feeder route; i.e., the aircraft would not be expected to overfly the feeder route and return to it. The pilot is expected to commence the approach in a similar manner at the IAF, if the IAF for the procedure is located along the route of flight to the holding fix.
Discusses: What to do when there is a feeder route from a fix on the route of flight prior to the holding fix.
In this example, a pilot plans to fly northbound to KMGM. They call clearance delivery and receive clearance to KMGM via V222 MONTGOMERY VOR. They plan to shoot the ILS 10.
Notice there is a feeder route from ALOON. If the pilot is on V222 heading north toward ALOON when they receive clearance for the approach, they will be expected to use the feeder from ALOON instead of overflying ALOON and proceeding all the way to MONTGOMERY VORTAC. In this case there is a feeder route from the holding fix as well, but that may not always be the case.
Paragraph 5-4-6 c
If a route of flight directly to the initial approach fix is desired, it should be so stated by the controller with phraseology to include the words “direct . . .,” “proceed direct” or a similar phrase which the pilot can interpret without question. When uncertain of the clearance, immediately query ATC as to what route of flight is desired.
Summary: If a pilot would like to fly directly to an IAF without using a feeder route, they can request to do so. The clearance must contain the specified phraseology.