Why the encoder matters at all
The JPEG standard specifies how a file is decoded. It leaves considerable freedom in how one is produced: which quantization tables to use, how to round coefficients, how to order the data, whether to search for better choices.
Encoders exploit that freedom differently, and the spread is significant — comfortably more than the difference between quality 80 and quality 82 that people spend far longer worrying about.
Crucially, every one of them emits a standard JPEG. There is no compatibility question: the output opens everywhere, in everything.