For the large majority of the population, download means "get it from the internet" which is what Websters says. For them upload means "send it to a website" which again, agrees with Websters definition.
So no surprise that Wikipedia's definition is based on what the words mean to a large majority.
I found this on the web, but am not an IEEE member so I can't confirm
IEEE Std 610.5-1990. IEEE Standard Glossary of Data Management Terminology.
download (A) To transfer some collection of data from a computer memory to another storage location. (B) To transfer
some collection of data from the memory of one computer to the memory of a second computer that is relatively smaller
than the first; for example, to transfer data from a mainframe computer to a microcomputer. (C) 610.5-1990
upload (A) To transfer some collection of data from some storage location to a computer memory. (B) To transfer some
collection of data from the memory of a small computer to the memory of a relatively larger computer; for example, to transfer data from a microcomputer to a mainframe computer.