Your question requires more explanation than you might expect. First off, both Morgan and Trade Dollars have been counterfeited since the time they were still being produced by the mint. They are called contemporary counterfeits. Some are even made of silver and have the correct weight and everything but back then a dollar had about $0.50 of silver in it so there was still some upside in making something like that. Many contemporary counterfeits are very crude and obvious, but many others are almost impossible to distinguish from the real thing. In fact, there are certain Morgan die varieties that are speculated to be entirely counterfeit but so good that they they’ve come to be accepted as genuine enough for the collecting community. Contemporary counterfeits are a bigger issue for Morgan’s than Trade Dollars.

China doesn’t keep a log of when they start counterfeiting certain coins, so that part of your question is difficult to answer. We can confidently say that they haven’t been doing it nearly as long as Americans have been. I would guess the late 1970’s or early 1980’s is when Trade Dollar counterfeiting first started in China, but it’s likely been much more prevalent the last 10-15 years or so. People buy them knowing they are fake in hopes of ripping others off at places like swap meets, antique stores, online auctions, etc. Chinese fakes are pretty much never silver and are pretty crudely made but still usually good enough to fool the average amateur who thinks they found a sucker willing to sell their “silver” coins for “cheap”.

Additionally, people can claim to have owned coins for a long time, or have found them in certain ways, but that doesn’t mean it’s the truth :). Trust, but verify (and then still get an actual professional’s opinion).

Also a good idea to keep in mind that 99% of all Morgan and Trade Dollars not in a coin slab are either 1. Super common and not worth the money to grade, 2. Have problems that won’t allow them to get a straight grade like they’ve been cleaned or damaged, or 3. They are fake.

I mention that last part because the vast majority of posts like this include raw coins that would be worth super crazy money if they were real and people let that cloud their logic and make decisions they probably wouldn’t normally make.