Inset describes the door type. According to the attached article door style refers to the type of panel, they refer to 4 basic types including recessed which can be called Shaker among other things. What may impact the price is the method of construction - how the frame is joined and the material in the recessed panel and how it is finished. My understanding is that you want the recessed panel to be finished before assembly (at least partially) so if there is movement in the frame what gets exposed will be finished. I am under the impression that it is better if the recessed panel is either MDF for a painted finish or veneer over plywood\MDF for a stained finish (this will also provide a more uniform appearance on the panel) as this will usually mean the door will contract or expand less in its' frame than if the centre panel is made of solid wood. If doing a painted finish you could go to a solid MDF door which can be routered out to look like a recessed panel but be one solid piece that is not subject to the natural movement of wood (MDF is more dimensionally stable than solid wood). My Mom went with a thermofoil finish over a solid MDF door - one of the characteristics of an MDF solid door is rounded interior corners - the routered groove in this particular company's product helps visually disguise it but if you look closely you can see the corners are all rounded. Here is a link that might be useful: door style breakdown

You have recessed panel doors but they are not shaker, since they have that detail. That part of the door frame, the stiles (vertical) and the rails (horizontal) that hold the panels in can have various profiles on the inner edge. This is called the "sticking": The new shaker door you show has Square Sticking. The doors in your house might be Ogee but they seem to have an extra curve, so might be Cove and Bead Sticking. The three dimensional panels might have Anaglypta or Lincrusta, which is a typed of embossed wall covering on them. The triangular plate on the door is called an escutcheon, backplate or sideplate.

Would they be a functional faux pas? Have you handled them in person? Are they easy to grip? Easy to clean? Easy to use to open a large heavily loaded drawer/ Do they hurt when you accidentally bump them? The wrong answers to these would make them a "no" for me. I've never seen these in person, so there might not be any issues, but I would want to find out before I committed to a full kitchen of them. I changed the pulls I was going to use in my kitchen because of a functional issue I found after getting a sample pull.

This is a beautiful kitchen you posted. I am considering the same thing, refacing my lowers with painted Barker doors and using Ikea cabinets for the uppers. I cant afford a 6 figure kitchen and I like what I see. Ignore the nay-sayers. Those are always the same people and they are really annoying and usually unhelpful. As whether this would bother you. some people will be bothered, but it really depends on whether it bothers YOU. You are the one who will bein the kitchen. Good luck.