Oh - this is going to be a big deep breath.
Me and my colleague (a concert pianist) produce speciality musical products - music for ballet, and kind of accompanist karaoke for people studying horrendously complicated music for Diploma level stuff. The practice with our tracks before moving to a real person for the exams.
He has C3 Yamaha, and our first product took forever because of re-take after re-take, and as he tired it got worst. Now we produce his piano sound inside the computer - Virtual studio Technology instruments - VSTi which are applications that sit on your computer and if you use Cubase, or one of the other popular DAWs, you connect your Yamaha to the computer, and the MIDI cable (which as I'm sure you know, doesn't actually carry any sound) tells the computer what you play. The VSTi could be a Steinway Grand, or a Bechstein, or Bosen...... or anything. Some people even use VSTis that are very specific historical instruments - carefully sampled and recorded for you to have on your system.
Your Yamaha just sounds like what it is, a freestanding electronic piano trying to sound like a grand. in the room, with it's little speakers it's not too bad at it, but connect it to a recorder and it's VERY unlike a real piano sound then.
The workflow we use is like this - He plays a weighted keyboard at his house on his Cubase system - he uses Cubase Artist. We both have the same set of sounds - and while I have others, we use a VSTi called Pianoteq. Very realistic and they sound right to him. He then sends me the track, and I fix it. I sort out little tiny slips and mistakes. Then he comes to me and we go through it again and make small changes. We also edit out the shorter versions we sometimes need. We then add a location specific reverb. Our recordings get played in very live spaces, so we have quite a dry recording so it sounds right in dance studios. We actually have three we use to test - all with different acoustics.
For you - I assume you do not yet have a DAW. I would recommend you download a trial of Cubase and try it out. It isn't simple, but it's scoring editing is OK - not remotely Sibelius, but editing notes on a stave can be handy. You need some kind of MIDI interface to get the audio in and out, and the MIDI in is dealt with by the interface too. You could of course send the MIDI back to your Yamaha for it's sound system, but once you have played some of the VSTi sounds you will not want to do this - a real backwards step.
You need:
Computer
Interface
Software
VSti for whatever sounds you want.
We have piano, orchestral and other traditional sounds. We rarely need synths, electronic sounds or weird noises. Somebody producing club music won't want a Steinway, or bassoons, a viola section or a classical choir.
Pianoteq is not the most expensive.
Real piano
Pianoteq
I like the Pianoteq better, personally.
Does this help?