WordPress Setting API – There is no field in options.php

in register_settings you need to pass the names of the options you use. right now it seems like you left that call the same as from wherever you copy & pasted it (not criticizing at all here). If you need two options (why?) then you need to call it twice, once for each option.

The option name is the second parameter to the function, the first can be whatever you want but it needs to be the same with the one which you will use in the settings page itself. Best practice is to use the slug of the settings page in which the settings will be changed, to ensure it is unique and make it easy to identify the context.