Generally, the term liner and the term insert mean the same thing. A liner/insert plus the cabinet surrounding it that replaces the outside skin of a metal hood should be considered the hood assembly. The liner/insert should fill the cabinet that surrounds it, or else some means of blocking grease from passing into the gap between the two components is needed. Off-the-shelf liner/inserts may constrain the cabinet size. In any case, you want the liner's aperture (capture area) to overlap the cooktop as much as feasible.

The insert comes in one size - and can work for a 30 or a 36 inch hood. The liner would be made for a 30 or 36" hood. Easier to show you if possible:)

Here is the underside of my hood:

Here is the vent insert - I used a Broan 390 - could be used for a 30 or 36".

The surrounding metal is the liner - which comes in various shapes and sizes. Some are T shaped and some are rectangular depending on the shape of your hood. This page list some different sizes and specs:

http://www.kitchensource.com/range-hoods/na-090as36sm1.htm?p=NA-090AS36SM1

There are a few different companies that make vent inserts and liners.

The CFMs required of your vent depends on your range. Professional style ranges often require more than 400 cfms. If you go over 400 cfms, you will need to have a "make up air" system too - which can get expensive, so don't go there if you don't have too.

For complete containment of the effluent captured by the hood, the flow rate depends on the hood entrance aperture and the velocity of the uprising cooking plumes. An actual specific flow rate of 90 CFM per square foot of aperture should be sufficient for baffle style hoods where there is an appropriate amount of capture volume for the baffle area. Blower rating has to be higher; a multiplier of 1.5 may be sufficient.

The hood insert pictured above appears deficient in several respects. It would take too long to describe all of them tonight. Aim for hoods that, within the bounds of aesthetics and practicality, approximate commercial hoods. It is the collecting (hood entry) aperture that must overlap the cooking zone, not a collection of flat sheet metal providing zero capture or containment functionality.

My hood is for a very ordinary 30" range with ordinary cooking - no grand chef here. For my purposes, the insert has worked fine.

Not to mention that it’s a fire hazard.

An ordinary range, or even a single hot plate, can raise a pan's temperature to the evaporation point or even smoke point of oils and greases. If this greasy effluent is to be captured and contained -- rather than deposited on walls and furniture -- both the hood air flow rate and the capture overlap have to be sufficient.

The apparently widely-believed concept that modest ranges require modest ventilation is only true if the cooking temperatures are also modest. By this I mean boiling eggs, making oatmeal, cooking vegetables in water, and other such activities where grease is absent or remains in a liquid form without evaporation or smoking. In such an environment, ventilation may keep down steam condensation, but is otherwise optional for keeping the residential environment free of grease. At higher temperatures, effluent velocity overwhelms the modest hood.

And Sophie's point is worth considering, even if there is no code violation due to having sufficient distances to combustibles -- something we can't determine from the image. The image suggests that not only can grease accumulate on wood parts, but some wood parts themselves are directly exposed to cooking heat, and the possibility of an unplanned flambé.

IMO nothing with wood around it above a cooking surface is never a good idea even cabinets above the hood get gross .

No wood portion of any hood should be lower than 30” above a cooking surface. No wood anything should be exposed to collect grease even above that distance. Grease will damage the finish of the wood and it will gum up and become unsightly over time. Not to mention be s horrorshow to clean.

Thank you all for the responses