Why do I get different results from Mac's shasum than from other shasum calculators?

The input to the shasum invocation in the question is test\n (with a newline), not test.

If you give test with no newline to shasum you’ll get the same output as the online tools you cite:

$ echo -n "test" | shasum -a 512
ee26b0dd4af7e749aa1a8ee3c10ae9923f618980772e473f8819a5d4940e0db27ac185f8a0e1d5f84f88bc887fd67b143732c304cc5fa9ad8e6f57f50028a8ff  -

By the way, I think there’s nothing special or MacOS-specific about the shasum found on MacOS; I think shasum is part of the standard Perl distro— installed along with, e.g., the perl command.

Try this:

hexdump -C <<< test

Knowing Unix shells, you're probably getting an unwanted 0x0a at the end of that string.