The 350 Chevy has always been considered a small block. Other displacements that are small blocks include 265, 283, 302, 307, 327, and 400, as well as a few other sizes produced by GM. All of those engines occupy more or less the same outward space, but have different bores and strokes. I think they were called small blocks because a few years after Chevy introduced the 265, they added another engine that had 348 cubic inches. That engine, and its big brother introduced a few years later at 409 cubic inches, looked much larger under the hood than a 265 or 283. So the terms big block and small block got popular when referring to Chevys. It was quite a few years later that Chevy introduced the small block 350 and 400, which had larger displacements than the smallest big block, the 348.
About 10 years ago, GM introduced a new engine to replace the Chevy small block in trucks and some cars. It is really quite different than the original small block and uses heads that look like they should fit a small block Ford.
In the mid 60's Chevrolet introduced a new big block that was quite a lot different than the 348/409. It originally had 396 and 427 cubic inches in cars and used very different heads than the 348/409. There were also medium duty truck versions of the big block with the smallest having 366 cubic inches and the largest 427 cubic inches. The later big block grew to 454 cubic inches in 1970 and is still in production in some larger sizes by Chevy.
Ford had several different engines during the same time period. Ford small blocks are generally considered to be 260, 289, 302, and 351 cubic inches. Ford big blocks include the 332, 352, 390, 410, and 428 FE engines and the completely different later 429 and 460 engines. Ford also had a medium block engine displacing 351 and 400 cubic inches.
Chrysler small blocks trace their heritage from 1955-56, but generally are thought of as the LA engine family, which started with the 1964 273. In 1967, Chrysler converted the 318 line to using LA heads and added a very high performance 340 engine in 1968. A 360 cubic inch version was added in about 1971. 318's and 360's were produced in trucks way up in the 90's, although they used many different parts than the early engines. The Chrysler big blocks started in 1958 at 350 and 361 cubic inches and in 1959 a 413 raised block engine was added. Other Chrysler big blocks include the 383, the 400, the 426 wedge and 440. Chrysler quit producing the big block in 1978 or 1979. Also considered a big block, the 426 hemi was based on the 426 wedge, with special high performance heads and many other modifications. It is still possible to buy a brand new 426 hemi from Chrysler. The current production Hemi that is used in pickups and some cars is a very different engine than either the classic big or small block Chryslers.
Buick had small and large block engines, while Cadillac, Pontiac, Oldsmobile and AMC small and large displacement engines looked more or less the same from the outside.
When the early small blocks were designed in the 1950's, I doubt that the designers had any idea that their engines would ever get to be as large displacements as they did, or that those basic designs would continue to be used for 40 years. The automakers continued to do what worked, and what made them profits.
The big blocks were designed at a time when the cars they were made for were getting bigger and heavier. Apparently at that time, the automakers had not figured out how to enlarge the small blocks, like they all later did. And I suppose they did not know just how large the market would demand engines to get. In 1970, many cars could be ordered with 429 to 455 cubic inches.
But then came the fuel crisis of the mid 70's. Big engines take lots of gas, and big cars also take lots of gas. Most large cars were downsized of disappeared and few big blocks were offered in cars after about 1978. The need for large engines continued in trucks, so Ford and Chevy kept offering big blocks in some pickups.
Most legitimate muscle cars of the 60's and early 70's had big block engines. They would not have been possible except for the fact that the manufacturers were already producing the large engines for use in the big cars of the day. In an intermediate size and weight chassis, those cars accelerated much better than people were used to. The muscle cars sold very well, until the insurance companies decided they were too dangerous and made the muscle cars too expensive for the average person to own.
So that is a short history of the small block and big block designation. Your 350 is a classic Chevy small block, although it is a fairly large version. Chevrolet made MILLIONS of them over the years. I don't know if it is still the case, but a few years ago, the 350 Chevy was considered to be the absolute cheapest automotive engine of all of them to rebuild. Good luck with your truck, and always keep on learning. Hope I haven't bored you too much!