GUEST,Phil d'Conch
Yes, I spotted that during my searches, together with info about some of the excursions being made, such as Here
This might explain Guest: Sid Gilbert identifying the engine as a Mohawk (with relevant wheel config.) It seems the 4501 is used for modern day excursions using the "Lonesome Pine Special" 'train'.
There is a distinction for rail enthusiasts between 'train' and 'engine'. Although they are often discussed as one and the same.
From what I can find it appears that, 'historically' the "Lonesome Pine Special" was the engine #1298, and a series of coaches.
But 'train' (as in the flowing attachment behind a bridal dress) can also be used to describe just the group of carriages being pulled by the engine.
Train can also mean the whole thing, engine + coaches, similar to a 'wagon train'.
And when someone mentions a "Steam train" it is quite possible they are just referring to the engine alone.

I hope this clears confusion in the previous comments, which, although conflicting, may all be accurate.