I would have said real world and speedtest are two totally different thingsspeedtest.net
in my experience is a good reflection of what your service is capable of. I took it to mean, "real world" compared to the quoted speed when you purchase it.
Why do they always report in Mbps?
Services are usually sold in Mbps, so tests are the same so you can tell how close to your theoretical maximum the service actually is.
I guess you might ask why services are sold in mbit/sec instead of MByte/sec; my understanding is it dates back to analogue modems, which would typically have to send 10 bits to communicate 1 byte (8 bits plus a start and stop bit). The raw communication link would carry X number of bits per second, and then the protocol on top of that would determine how many bytes would get through.
The same is still true today, for different reasons; you wont get 125MB/second on a perfect 1000mbit link. Due to various overheads in TCP/IP and so on, its more like 120MB/sec. Reporting the link as 125MB/sec would thus likely lead to confusion about why you dont actually get 125MB/sec downloads on that link.