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

Recessed panel refers to any door style where the panel is recessed. Shaker style if one type of recessed panel door. The cost of the door will differ based on: 1) whether the panel is solid wood reverese raised panel vs. veneer vs. mdf; 2) the intricacy of the details on the door such as beading. I'm attaching a link to one site that shows several recessed panel doors. Caryscott is somewhat correct that a stained veneer with give a more uniform appearance HOWEVER a veneer will not age the same as a the wood frame (for example, the maple frame will yellow with age - the veneer will not).

If you are getting stained cabinets and can afford the upgrade to solid wood reversed raised panel, then for my money that's the way to go. The door feels more solid, will age the same and adds value to the kitchen.

Here is a link that might be useful: Recessed Panel door styles

Thanks..I was planning on having the cabinets painted white. So do I want veneer or solid.

I don't work in the cabinetry industry in any capacity but it was my experience when trying to decipher what means what in relation to cabinetry you have to do a lot of research and arrive at your own bottom line. My feeling is that the differences between materials, finishes and methods of assembly are sometimes not as clear cut as some would have you believe and you need to consider your pattern of use, location and needs when making your decision. Personally I do not understand paying for finish grade wood and having it painted - if you intend on having an opaque finish I would go either with a paint grade frame and an MDF panel or a solid MDF door. If you live in an area where there is a lot of humidity solid MDF might be better, if the kitchen is going to be used by kids and teens I might lean more towards wood as it will hold fasteners better and be more dent resistant. Unless you live in a very arid climate I do not think a solid centre panel and a paint finish would probably be a good idea but I could be wrong.

When looking at lacquer finishes on recessed panel doors at a custom shop we were shown examples and told to expect hairline cracking at the mortise and tenon joints and around the recessed panel.

Here is a link that might be useful: thead discussing painted doors

I would ask the cabinet maker to spell out the differences and what affects the cost - it likely will vary from company to company.