I'm totally newbie in printing production and now I need to print something that requires high color correction (be as close as possible to the colors on design file). So what color palette should i send to the printer: CMYK or Pantone? If Pantone is considered as "standard" in matching colors so why people don't design in pantone but still in cmyk? Thank you!
Pantone is a company that created various colour matching systems for the printing industry, There are Pantone colours that are CMYK (process colours), and there are Pantone colours that are spot colours made from mixed inks. So, your question doesn't really make sense. I assume you actually mean Pantone Spot colours
CMYK printing uses four colours of ink (cyan, magenta, yellow and black), sometimes also called full colour process printing, and it requires four printing plates, and often a printing press with four colour heads, or perhaps even two passes through a two colour press.
If you add a Pantone spot colour, and also want full colour process printing on the same sheet (for printing photographic images for example) - that would be five colour printing, and that would be more expensive. It would require an additional print head, or an additional pass through the press, and an additional plate, etc.
Pantone spot colours are often used in printing commercial stationery, for example when you have a logo that is only one/two colours, and when process printing is not required. Printing in only two colours is often cheaper than printing in process colours. Spot colours also look better than process colours up close (see illustration below). This is especially true for small logos, or small coloured text, or line art.
Spot colours look quite different from process colours. Essentially, spot colours are made of solid ink, which is mixed by the printer to a formula guide, whereas CMYK colours are made up of different coloured halftone dots. So it's really a different printing process.
TLDR: Whether you choose CMYK or spot colours would depend on what the client wants, and what their budget is, and the kind of printing required. It's also possible to have both CMYK and spot colours.