Right next to you, within arms reach.
(My cat is near me.)
Down the street or within a few blocks or so.
(A Walmart is near me.)
Hundreds of miles away, but relatively near if you compare it to a much farther location on Earth.
(New York City is near me, if I am interacting with someone from U.K. Or Europe, or Australia, etc )
Belief in the honesty and reliability of someone or something
An arrangement in which someone's property or money is legally held or managed by someone else or by an organization (such as a bank) for usually a set period of time. (Merriam Webster)