is the sound of vinyl due to the physical process of the turntable?

A turntable introduces rumble and wow.  Rumble is the noise from the turntable and wow is the change in speed from the needle being dragged through the record groove.

Whereas digital is digital, not much too talk about. 

You're wrong there.  There are many flavors of digital to enjoy and digital sound quality is progressing steadily.  All vinyl does not sound better than all digital, either.  Good digital can sound as good as good vinyl.  If anyone prefers the sound of vinyl, though, that's fine with me.  We all like what we like (see Geoff).

I find the area where the greatest improvement can be made is in recording quality.  So many albums are just not recorded very well. 

@theo @mrubey  It all starts with recording the actual instruments in studio.  Everything is recorded digitally theses days.
Technically, the best medium is digital and by far: Much Higher Dynanics, much better separation, much lower noise, no wear out, no angle error, no medium saturation, no compression, etc etc etc.  The Vinyl is highly processed to fit in the physical medium.  There is the RIAA EQ Curve applied so it can sound decent on this very poor medium.
And contrary to what you said, there is no "lost information" with digital, it's simple math theory at work.
All that being said, you are perfectly right to prefer the sound of one or another, digital or analog.  Each component has its transfer function, at the end, whatever it is, you are the one who listen and choose.

Personally, i have a decent DAC with a matching intergrated amp and speaker, i love the sound.  I'm really not looking back to vinyl, that's for sure!  But that's just me.  I listened to many HiFi soundsystems for the last 40 years: Linn Sondek, JA Mitchell, Classé, Mark Levinson, Naim, Snell, Magneplanar, KEF, Wadia, etc etc etc.  While they sounded very good, for me nothing beats a high quality digital playback with a good DAC and matched component.  Happy listening!

I recommend if your happy with digital don’t listen to vinyl or tape. Hearing vinyl on occasion probably won’t sway you. But if you spend much time with it your brain gets used to the natural sound and you will then be less likely  to be satisfied with digital. Then you’ll always be trying to get your digital to sound like vinyl. Vinyl listeners don’t seem to be wanting  their systems  to sound like digital. I find your brain can adapt and get used to digital if It wants to and even find it enjoyable. This is just my opinion from my own personal experience of 30 years since my first high end Esoteric CD transport and DAC from 1990. I haven’t owned a digital source in 6-7 years now.

Try not to listen to systems that are better than yours. That will only depress you. Only listen to systems that are worse than yours. That way you can avoid the upgrade urge and the tweak rabbit hole simultaneously. Keep telling yourself, my system sounds fabulous! 🤗