Obtain RGB & CMYK from Pantone Color: "edit artwork" vs. Pantone Color Finder?

Working with a client whose logo has been designed and Pantone colors are set.

Along w/ the PMS colors,  the “corresponding” CMYK and RGB colors provided by client coincide with what the Pantone Color finder says for each swatch.

https://www.pantone.com/color-finder

However, visually the PMS suggestions for CMYK and RGB seem off.

When I pull the PMS colors up in Illustrator and use the edit > edit colors > recolor artwork option for either CMYK or RGB (depending on document color mode) Adobe’s suggested colors are different from what the Pantone color finder provides.

Admittedly, the Adobe colors look like a closer match for both CMYK and RGB, but I’m wondering which would be closer to a match?

My CC apps are all synced via bridge to the North America General Purpose 2 profile, but even pulling up a cmyk document w/ the pantone swatch in Photoshop actually labels it a different Pantone color (from Illustrator and Pantone's suggestions)

Do I trust my eye / display for RGB and trust Pantone for CMYK?

Here are the specs:

Color1: PMS 4975 C (Solid Coated)

Pantone gives it the following values:

PANTONE 4975 C - find a PANTONE Color

C=36 M=84 Y=59 K=85

R=63 G=32 B=33

While Illustrator “recolor artwork” gives it the following values:

C=49 M=78 Y=69 K=67

R=65 G=32 B=32

For the brown color, the RGB is a closer match but the CMYK that Pantone suggests is noticeably darker.

Color2: PMS 294 C (Solid Coated)

Pantone gives it the following values:

PANTONE 294 C - find a PANTONE Color

C=100 M=69 Y=7 K=30

R=0 G=47 B=108

While Illustrator “recolor artwork” gives it the following values:

C=100 M=86 Y=29 K=2

R=0 G=46 B=109

For the blue color, both Pantone suggestions seem way off when compared to Adobe’s suggestions.

Thanks in advance for any advice or "best practices"...