Honestly I'm not 100% sure what the Internal Storage wipe does under Advanced Wipe, and I don't feel like making then restoring a backup right now just to test it
. I never use it. If I had to guess, I bet it wipes /data and possibly a few other partitions without preserving user files in /data/media/0, see below, but don't know that. It certainly won't blank the whole internal storage; some areas like recovery, modem, and aboot are far too important and won't be touched.
Here's what I can tell you. Doing Wipe -> Advanced Wipe -> system, data, cache, dalvik is typically good enough for flashing a new rom (switching from Touchwiz to AOSP can require some additional care), some would even say overkill the way rom installers are scripted today, but old habits die hard. However, Advanced Wipe -> Data will wipe /data without wiping /data/media. Since android got multi-user support, files reported to be in /sdcard are actually stored in /data/media/0 for the primary user, so that means that downloads, pictures, user app files and things like that can be left behind by just wiping data since /data/media is left untouched. It is useful if you don't want to shuffle your files off then back on the device to flash something new or if you're using a device without an external SD and have a rom zip stored on device in /sdcard, but it leaves stuff behind if you're looking for a clean start.
To completely blank /data pick Wipe -> Format Data and TWRP will format /data and leave nothing behind, not even /data/media like the normal Advanced Wipe -> Data preserves. Just make sure you're prepared for the phone storage to be blank. You'll have to flash from external SD or push files from a computer over usb. TWRP does automatically start up mtp and adb shortly after booting if you need to push files over usb.
/system is a partition of special reserved space just for the rom and system apps and not user files. It is usually mounted read only when booted up normally to keep us from messing anything important up. I hope this helps and doesn't just muddy the waters more.