Illustrator | working space is not the same as export in CMYK

[.367118080e06]

Hi,
would highly appreciate the help, was not able to find any relevant topic. I guess I'm missing something obvious.

Problem
I created a file in RGB, then swtiched to CMYK and started using Pantone Solid Coated which are required by the printing house.
The problem is that although Document Color Mode is CMYK, my exports in JPG look different. They are shifted towards grey. PNG exports, on the other hand, look exactly as on my working space. I assume JPG shows true CMYK, while PNG doesn't and that means my working space somehow is not presenting true  CMYK colors. 

What was tried
I tried to copy my work to brand new file (CMYK from the start) and it didn't change it.
I also tried setting workign space RGB: Monitor RGB and CMYK: Coated CRACoL 2006 (read online it should present more true colors in CMYK). None of it worked.
I checked on different computer and monitor the same file and the problem was exactly the same.

I read that maybe it has to do with swatches. Is Pantone Solid Coated is not CMYK? And does working space not automatically adjust colors? If yes, it would mean I'm using wrong colors and should go for Pantone CMYK Coated?

[.367118080e06]

Why there is no way to edit the post?
Anyway, answering to my last question.  Even changing to Pantone CMYK Coated, export is still different to what is in working space. Here is picture. M stands for monitor, Ai for Illustrator working space.

[Ton Frederiks · Accepted solution]

Pantone solid colors are spot colors; mixed inks that can be used to print colors that are not possible with CMYK inks.

Image formats like JPEG cannot have these special spot inks, and in the case of png, it can only save RGB..

Use PDF files if you want support for spot inks.

[.367118080e06]

Thank you for answer, that clarifies usage of Pantone colors.

However, If we consider now situation without using pantone colors and using only CMYK swatches I still have problem with representation of CMYK.
In working space colors are different than on JPG or PDF. 
PDF is brighter while JPG darker and more greyish.
What may be the problem?

By the way, when using color wheel while working on CMYK working space it should allow me to only use colors that are within this scale. Is that correct?