HI -- A kitchen remodeler - just designs and installs kitchens .... A design build is a designer/architecture and contracting / construction ... you need the design build for your project because you are changing structure etc.

How do I know if a firm is a kitchen designer or a design/build firm?

I have interviewed 6 firms so far and everyone said they can absolutely do the work. However, I don’t think all of them were design/build firms, because they were all listed under ‘kitchen designers’ in Houzz, and some of them didn’t have an in-house architect.

A design-build firm simply means that it designs and builds, no need to hire a separated designer.
A kitchen remodeled usually specializes in kitchen and many times in bathroom remodels as well (due to the similarity). Most remodels are of bathrooms and/or kitchens, these firms can usually handle other projects as well but have the most experience with kitchens.
Many design-build firms don’t necessarily have an in house architect, engineer or even a designer. They just bundle it together for you so you have a single entity to deal with.
We offer a cradle to grave project management, that means we handle your project from “I want to remodel my house...” to final touches such as silverware in the kitchen drawers.
We handle design concept, architectural plans, permit and planing process, construction phase, landscaping phase and furniture selection, purchase and installation.

Then I guess all of firms I had interviewed are sort of design/build, except 1 firm who said he will do construction only.

IMO you need both the design build for all the structural stuff and a KD for the actual kitchen design and I agree you need to check their references thoroughly and often the firm has a KD on staff.

I'm not a professional and a lot depends on where you live, but I am struggling with how you can do all that work for $100,000. And I'm surprised that no one else has commented on this.

Narrow your focus to one single project. And figure out if you want the designer reporting to you or to the builder. Do you want your kitchen? Or what’s the easiest and cheapest for the contractor to do?

@shevice yeah, we know it is a big stretch. We plan to do lots of stuff (e.g. demo, recess lights, door knob changes) ourselves and hold some expensive items like foyer chandelier for later. We decided not to replace the trims, too.