Faith,
"..So trace routing on a workstation will take the same hop as performing a trace routing while logon to a router.."
No, not necessarily. The idea is correct but a traceroute performed from a cisco router can be directed from any valid
(that is logically addressed) interface, from any number
of origin ports, with variability in setting ttl, wait intervals,etc..
The path(and therefore:=hops) your packet takes depends on too many variables to really give a pat answer to.
But basically no. A traceroute from a router will
not give you the same exact information.
Furthermore, tracert, the windows utility, is not
really compliant and may give you very different results in certain security scenarios.