You have seen and no doubt read about DAW’s within the threads here, Logic Pro, Ableton, Steinberg, Cubase and Garage Bang to name but a few.
Cakewalk is a fully fledged DAW that was marketed as Sonar and when Cakewalk went defunct the DAW element was taken over and is now marketed as Cakewalk.
Bandlab is a cloud based musician collaboration and it is them who offer Cakewalk foc to registered members of the site which is also foc.
Now Audacity is also free but it is an open source program which is constantly being developed by a consortium of programmers.
Audacity is best thought of as a single track recording app, since it receives the analogue audio signal from the PC input and records it onto a single track. Audacity is also a multi track recorder but for now just make a mental note of this.
Once the single track recording is finished you can then process the waveform by the likes of normalising it, reducing noise, applying filters in fact whatever you want. Or you can simply output the track as an MP3, WAV etc. It will also rip a CD to produce an MP3 file of each track, it will also convert one file type like AIFF to say MP3.
Audacity is a very powerful and useful bit of software that personally I have been using in my Non Linear Editing video workflow for many, many years. It is what I have been using to record commentary and I use it to reduce background noise that has been recorded by my camera’s mike.
A DAW does not record analogue signals, it records the notes generated, their duration etc in effect it is a digital keystroke recorder. Typically 16 tracks where each track is used for a separate instrument voice.
Connections.
Audacity is best supplied via analogue audio, so it is the line outs from your Yammy S to the line inputs on your PC. The line output on your S 550 is via the headphone socket which looks to be a standard 3.5mm TRS, now as far as the input on your computer is concerned it may well be the same or it may be via two phono sockets (these are also known as RCA sockets). If you cannot ID, can you take an image and post it?
MIDI, your PSR does not have MIDI sockets, MIDI is handled via the USB host socket so a standard lead like one used to connect a printer is all you heed.
Hope this helps.