> did I just create a derivative work of "ls"?
No, output of a program isn't the program itself, so it doesn't fall under copyright[1]. Why would you expect that it would be a derivative work? It should be obvious that e.g. when gcc outputs a compiled program it doesn't automatically become tied to the GPL.
The only exception - which is mentioned[2] in the GPL - is if the output of a GPL licensed program is part of the licensed program. (quines, other rare utilities)
2. Basic Permissions.
[...] This License explicitly affirms your unlimited permission
to run the unmodified Program. The output from running
a covered work is covered by this License only if the output,
given its content, constitutes a covered work. [...]
> would my program that calls [a library derived from GPL licensed program] also be a derivative?
Probably[3], but see the FAQ[4] for answers to common situations and a real lawyer for actual legal advice.
> does one form of calling create a derivative and the other form not?
Correct. They are different. The intent is that the GPL licensed code is still open. Users that receive copies of the new stand-alone executable can exercise their right to examine and modify that code. They can easily replace it with a version they have modified without touching your other programs that merely use the output.
[1] https://www.gnu.org/licenses/gpl-faq.html#GPLOutput
[2] https://www.gnu.org/licenses/gpl-3.0.en.html
[3] https://www.gnu.org/licenses/gpl-faq.html#IfLibraryIsGPL
[4] https://www.gnu.org/licenses/gpl-faq.html