Suspensory ligaments: why are they ligaments?
&quot;...The suspensory ligaments connect the ciliary muscle to the lens...&quot;

You must be referring to the Zonule of Zinn (Such a great name).
You are absolutely correct, the definition of Ligament varies across texts which can create confusion.
For example:
Merriam-webster:
A tough fibrous band of tissue connecting the articular extremities of bones or supporting an organ in place.
Wikipedia:
A ligament is the fibrous connective tissue that connects bones to other bones.