I don't find any of the language confusing or "odd" as others do. Although, the CMYK sentence being between the Pantone statements is just poor positioning. It should list all the Pantone items, then the CMYK items, not mix them. "CMYK Build" is a synonym for a "CMYK breakout" or "CMYK percentages".
(But the UK spelling of "color" is "odd" :) )
I read this as ....
If you used a Pantone color, specify the number, according to the Pantone Plus guide for best results. You do not provide Pantone numbers if you aren't using Pantone colors.
If you are using CMYK colors, supply the percentage breakouts. This was very common before everything went digital and before color management was very reliable. Its not that common today, but I've seen it a few time - Mostly for higher-end print runs. The printer is asking you to supply numbers rather than relying on any embedded profiles.
In areas of large solid CMYK color coverage you supply the percentage of each plate for the color.
This is just a way of not relying on color management really. If you provide percentage breakouts, they'll match those percentages. Therefore if C60 M6 Y40 K0 is NOT the color you see on your monitor, it's not their problem if the print uses those percentages. It's really a "CYA" technique for print providers.
You can supply something like this:
(Just a note, if you create an image like above, and are supplying it digitally, do not supply it it as a PDF or any remotely possible print format. Send it as a .png or even .gif, or crop it to a clearly unusable piece as I've done above, so it's not mistakenly used as a print production piece.)
For the orange gradients in the first image, supply the dark breakout and the light breakout.
In the old days, you'd have a color proof and use a pen or grease pen to write the percentage breakouts on the proof. You could still go this route as well.
This just helps the print provider match the colors you are seeing without relying on embedded profiles.
Truth is it's been a looooooooong time since I've had to provide breakouts unless a proof came back with the wrong color. Color management and ICC profiles are exceptionally reliable nowadays and essentially do this for you. But then, it's not impossible that a print provider has either included that statement to (1) "Cover Their A.." as I've posted or (2) are so far behind the times they don't use a color managed workflow or (3) they don't understand embedded profiles or (4) that's a very old part of the web site that hasn't been updated - at least the text anyway (it was a preferable way to work years ago) or (#5) they are an overseas print provider located in Asia somewhere. I see this with eastern print providers from time to time. My vote, would be for #1 .... they just want to cover themselves, maybe #4 if they've been around for 10-20 years or more.