Generally, as a designer, your only task is to let the printer know your working space. Tag or set intent when exporting your work.
- If the printer provides, recommends a profile for your job, substrate, design your artwork in that profile. Tag or intent your job.
- Unknown printer? Use a generic profile (for offset (Europe) for example Fogra 39, or v2 ECI) and let the printer know your profile used for the artwork (tag or intent).
- Device values are meaningless for the printer, they will assign their defaults or ask you about your working space.
- A good pre-press will warn you if they see something fishy (extreme out of gamut colors, shifts).
- For color critical work request a hard proof from the printer if possible.
"Lets say if the print house uses fogra39 and my files are on iso coated. There will be a difference from what I see on my screen, but I’m trying to understand will it be very visible, meaning should I be very worried in a case like this or not."
In theory, if you set a color in Fogra 39 and the printer assumes a different profile, yes you may see some difference (CMYK values remain the same), but if the printer converts (CMYK values converted) to a different space you would not see much difference assuming both spaces contain the set color in their gamut. If the set color is out of the target profiles gamut you can expect some difference.
Some toughts about Wolff's post since he linked his previous comment.
"A CMYK image is basically just a collection of pixels with each their CMYK values. They can have a color profile embedded (we say the image is "tagged" with that profile), but it's really just a name. The CMYK values have been determined when the image was converted. The profile doesn't do any additional trickery."
Yes CMYK values have been determined... without knowing the profile these device values are useless, you can say it is blue (80C/10M), but what blue is it exactly?
The blue your default printing house profile determines or the blue set in the artwork file characterized by the tag profile?
Really just a name? No, not really, they help you to know what blue it is in a device independent space.
"All print houses I've ever worked with (including our own) in the end don't really care about which color profile an image is tagged with."
Obviously this is not the way to properly handle color management...
"The CMYK values are used as they are as instructions to which halftone screens to burn to the printing plates. A 50% black simply becomes a 50% halftone screen on the plate. (There is also some calibration curve applied but that should be of no concern for a designer.)"
So if you print 50% black with different black inks made for various profiles visually will you get the same color when printed?
"The printer can't respect other profiles your PDF might have set as intent. And they certainly can't print different elements of your PDF with different profiles."
Sad, so what is the point of tagging and setting intents?
The printer can, and some will respect the source profile, because it is a must to do a proper color conversion if needed.