"In any relationship, the essence of trust is not in its bind, but in its bond."
This is, frankly speaking, a rubbish aphorism thanks to its inscrutability. The two words are near synonyms.
The words bind and bond are being used here in the following senses.
cause (people) to feel united:
the comradeship that had bound such a disparate bunch of lads together 1
impose a legal or contractual obligation on:
a party who signs a document will normally be bound by its terms
a force or feeling that unites people; a shared emotion or interest:
there was a bond of understanding between them
In other words, bind is being used to imply a forced connection thanks to external factors. Bond on the other hand indicates a mutually shared relationship. To attempt a little pithiness of my own, a bind is made while a bond grows.
1 This example is probably a bit of a grey area. You can be bound together because you are comrades. Your shared experience as comrades can also create a bond between you.