Likely Bachman sold original Williams for a while after they acquired them so just look at the box. It will say Bachman if they produced the product. The engines are essentially identical but some of the buyers of early Bachman noticed the gearboxes had little or no grease in them. A local club has had two Bachman engine failures due to worn gears. Williams used to sell the individual gear but now you are lucky to find complete trucks with motors should a gear fail.
Wikipedia says Williams was sold to Bachmann in October 2007. But I don't see any reason to avoid Williams by Bachmann if you like conventional operation and don't need the details that you get with Lionel and MTH. The ones that I have had are basically bullet proof.
On the Bachman site, the Williams & Bachman catalogs are listed separately through 2016 (if that means anything).
As Norton mentioned it's a fair assumption that "Williams" continued to build product for some time after the buyout. Why not use the existing molds, assembly line, staff, etc., to build the O-scale product. Perhaps cost cutting mandated by Bachman introduced some quality control issues (e.g., the missing grease). Completely new designs driven by the Bachman side of the house should be distinguishable from the original Williams line.
It's been said on MTF, that Williams drive trains are bullet proof. IIRC, that was certainly directed at the diesel drive trains. Not sure about the steam drives.
I started out with traditional size trains and have a fair amount of pre Bachmann Williams.
I don't run them a lot any more but have had zero mechanical failures and only one issue with a TBII sound board which had no bell sound. Their steam is pretty solid. I have the Berk, Turbine, and baby Hudson. They have the small Mabuchi 385 motor but I have run the 2056 with 5 K-Line NYC Anniversary passenger cars which are very heavy for two hours with no problem.
As an aside Lionel is still putting the same motor in their Legacy 2-8-2s with a list price north of 1200 bucks.
Me too, I have no issues with Williams and don't pay attention to what my box says. My Williams typically have less detail but I just got a U.P. Diesel and the detail is good. I run conventional and I believe all Williams create some sounds. I am an MTh fan primarily with Atlas, Lionel, Williams and some K-Line.
Never had problems with my W by B engines. Great runners, paint schemes not quite what I'd like, but repainting is an attractive option. Great runners, sound just okay, not great, but what runners and pullers! Will outlast most Lionel at double or triple the price, I'm betting... two of my Williams F units...