Sighax is a bug in the 3DS's bootrom, allowing for custom kernels (ie arm9 programs in .firm format) to be signed and therefore accepted by the bootrom
B9S is such a custom kernel (one which does little more than loading another from SD, ctrnand, or [thanks to another exploit it integrates and leverages] dumping the bootrom to SD if certain buttons are pressed) but there are others (GM9, fastboot3ds, Luma itself, etc can all be installed directly as a kernel)
To add to the confusion, while B9S is probably the most popular custom kernel, the original implementation of sighax (which never caught on, mainly due to lack of instructions) was called, well, sighax
In short yes, if you have B9S installed you're using sighax
If you want to update your console, the order in which you do things doesn't matter (as well documented in multiple topics for multiple years) - Luma 8.1.1 can't boot the newest 3DS operating systems, but since you don't need to boot the 3DS operating system to update Luma, the order is ultimately irrelevant
