Every stove top should have a hood ... not just appear to have one.

You need to talk to your builder/GC about this because you have to coordinate this with a couple subs. You need the cabinet folks and the HVAC folks because the ventilation system has to properly fit into the hood so everything looks right. Start with builder/GC. He/she should have advise on this.

There are also "code" requirements for distance from bottom of hood to stove top that have to be considered as well. Lots of little details on this type part of a kitchen project. Are you doing a "new build" or "reno"?

We're doing a Reno. Contractor said we need both, but I swear the appliance store we went to said we just need the liner if we are going for the "cabinet look".

That doesn't make sense. They are two different pieces. The so called "liner" is the vent structure around the fan and it generally comes with a hood designed for the size of the exhaust fan. Then the cabinet maker designs a wood cabinet structure to fit over this unit. So, if I am understanding you right, you will need both for a cabinet style hood structure and exhaust fan.

Here is example.

This is just example. There are a dozen details that need to be considered for a vent fan. The appliance store is probably just selling the vent itself (see inner portion of the photo above. The cabinet is made by someone else. The "duct" work for the venting is done by an HVAC company that does this kind of work. There are requirements for sizing based on distance to outside exit, bends in duct work etc., etc. Not a simple thing.

Got it. So we already went and picked out the vent itself and now just need to pick out the hood, like what you showed here. Thank you.

This can turn into a 4K-6K mistake very quickly if you supply the insert and the cabinet maker is not in on the selection. You need your GC and KD coordinating the cabinet maker, electrician, HVAC people, roofers, and trim guys. All are involved here.

Don't forget about the exhaust duct that goes from the hood to the outside. It needs to be 8" diameter. Ask your GC what is the diameter of your exhaust duct. If he responds "6" and that is fine", stand your ground and insist on 8" diameter duct. You don't want to force air through too small of a duct. That creates additional noise and reduces efficiency.

There is a lot you don't know on this subject at this point. A custom cabinet hood is expensive, and more complex than just buying a stainless steel hood that comes with its motor so there's no need to buy separate components. Before you plunk down that money for the custom hood, either get better educated so you spend the money on the correct parts, or buy a stainless steel hood.

BTW, the exhaust should have baffle filters, not mesh filters.

Much of what is stated above is true but the size of your exhaust duct is determined by the manufacturer and there are some new duct solutions to retrofit into spaces between studs you might want to explore. Long duct runs require supplemental fans along route to ensure proper air movement. And you thought this was going to be easy, right? Lol. Just take your time and ask lots of these questions.

"the size of your exhaust duct is determined by the manufacturer"

When you say "manufacturer" do you mean the hood's manufacturer? If so, your statement is true if the duct is already installed, and the homeowner cannot change it. It would be ideal if the homeowner could install the 8" diameter duct first, and then shop for a hood that uses an 8" diameter duct. Installing a 6" duct first means you are constrained by that size from the getgo. Most hoods that are 600 cfms or more need an 8" duct, and the hoods that do spec 6" or 7" diameter ducts will be noisier due to the physics of pushing air through a smaller space vs. a larger space.

If the OP's reno does not include ductwork, then she needs to look at what size is her existing duct, and shop for a hood that specs for that size duct. But if she has the opportunity to install the exhaust duct, she should insist that it be an 8" diameter duct.