The principal definition of trusty is meriting trust, trustworthy, or reliable. It’s almost always an adjective, but it’s occasionally a noun denoting a trusty person.
Trustee is almost always a noun denoting a person or organization. Its main definitions are (1) one that holds legal title to property in order to administer it for a beneficiary, and (2) a member of a board directing the funds of an institution. It can also be a verb meaning to place in the care of a trustee, but it is rarely used in this sense.
Examples
Trusty
With her trusty metal detector, Sue Beck has been digging up little Gloucester County treasures for a quarter century. [NJ.com]
Of course, Tintin’s escapades wouldn’t be complete without his trusty canine sidekick Snowy. [Daily Mail]
It hurts that no one even wants the millions of trusty old typewriters. [Edmonton Journal]
Trustee
Therefore the trustee could distribute all the franking credits to the resident beneficiary. [Sydney Morning Herald]
The trees on campus may not be put into a tree museum, but trustees for the College of San Mateo did vote this week to pave at least 20,000 square feet. [San Francisco Chronicle]
The tax overpayment, which has not yet been repaid, will go to the trustee of Drumm’s estate. [Irish Times]