ssheri72 , what you have there (top image) is known as a 'fob chain' (with a 'T' bar) .
A fob , such as for a fraternal organization , would be attached to the short end of the chain , with a pocket-watch attached (clipped on the clasp) to the longer portion of the chain ; the "T" bar would fit through a button-hole (typically in/on a vest) .