Macs do not come with "system audio recorder" - you installed it, intentionally or otherwise. Neither do Macs come with "Loopback Device" - it looks like you have been experimenting with different streaming recorders. Mac System Report will tell you who claims to make these applications.
Apowerstoft is usually regarded as malware - I would get rid of it.
To try Soundflower, use "Soundflower-2.0b2.dmg" as described on http://manual.audacityteam.org/man/tutorial_recording_computer_playback_on_mac.html
Please make sure you have copyright holders' permission before recording audio from the internet. This is a standard disclaimer to protect ourselves.
NelleB wrote:Really? My computer's audacity has a "system audio recorder" option on the devices bar thing. It's always worked fine before, and it won't work. I've been able to export and record streaming audio straight from audacity. I've attached a snapshot of what it looks like on my laptop.
I tried to download Soundflower, but it looks like it hasn't been updated in a few years because whenever I try to open the disk image for it my computer says it's too old to download. How are you using Soundflower?