From my own experience - it is not the same.
The ones you buy on e-bay from Hongcong are most of the time counterfeits. They, yes, are PIDs and they work, but they are not in agreement with the REX C100 manual, the names of the variables are different, and one of the two I bought is just totally different and the manual simply does not apply, and another one is kinda in agreement, but only kinda....limited compliance.
Also the guys simply misinforms you.
The one I bought that claimed to be with SSR output was with Relay output, and then when he sent me the one with SSR output - it was 220V one. When I told this to him, he said "no, don't worry, it is universal 110/220V". So when I plugged it in, it lighted up, but the temp measurement did not work, and I thought it was defective. Then I plugged it in 220V and it did work.
It is a mess. But still, I agree - you, most probably, will get something that works, and cheap. But - no guarantee it will, and it is a counterfeit, and even the manual (like the last one I got) may be in Chinese. Of course if you read Chinese - no problem there.