The model 35 was first made in the early 1930's. A completely different, re-designed rifle was first released by Diana in the early 1950's, and was made until the mid 1980's. It is a wonderful gun. It's a nice size and weight, extremely durable, good power, good trigger, excellent accuracy. As you can see from the other posts, it is a gun that people tend to hang on to.
The picture below shows a very early post-WW2 model 35. It has a tapered barrel, special target sights, and the stock and trigger are different from later guns.
Not to be argumentative, but the pic of the "Winchester 435" above is very typical of the standard model 35, as manufactured from the early 60's to early 80's. All Diana rifle models switched from red to black rubber buttplates in the late 70's, the red tending to oxidize and crack over time (though you are correct in stating that the 35S, made beginning about 1976, would typically have had the black one).
The model 35S had many other detail differences. The stock was generally more angular in contour. The fore end was flat on the bottom and had an angled front, not rounded as on the standard 35. The trigger guard was more angular and the trigger blade straighter. The 35S also had a 2-piece cocking linkage and an automatic trigger-blocking safety, instead of the simple single cocking link of the standard 35.
Yes, "Winchester" was a Diana brand name unique to the USA. Diana has sold many, many guns bearing the labels of different importers or distributors over the years. The famous US firearm maker Winchester tried hard to cash in on the interest in airguns by selling Diana models from about 1969 to 1975.
They sold the models 5 and 6 pistols (Winchester models 353 and 363), the models 16, 22, 23, 25, 27, 35, 50 sporter rifles (Winchester models 416, 422, 423, 425, 427, 435, and 450), and even the model 65 recoilless match rifle (Winchester 333). Each was stamped with the Winchester logo and model number.
Diana guns of this era were quite well-made and finished, and the Winchester-labeled ones are fairly common finds here. They usually command a bit of a premium price as they are also popular with Winchester firearm collectors.