They are usually much louder than ones designed for interior use. And those interior ones are loud enough already, unless you really want to get way up there in prices for silencers and remote blowers.

For the flow rates that should be used, an in-line or remote blower would seem to be a necessity. A silencer should be used between the blower and the hood. Your ducting may need to be 12-inch if the hood is very wide. Your make-up air has to be commensurately large.

@opaone writes about his commercial hood system in https://bamasotan.us/range-exhaust-hood-faq/ as well as Hood FAQ II https://www.houzz.com/discussions/6099827/exhaust-hood-faq-ii#n=71 and https://www.houzz.com/discussions/5745986/commercial-range-hood-install#n=120.

Commercial makes sense if there is enough height in the kitchen for the hood height because they require less CFM for typical residential hot oil cooking. Without sufficient height, the lower height BBQ hoods such as Wolf's "Outdoor Wall Hood" (see Wolf Design Guide) make sense.

The 48-inch Wolf has an entry aperture of 10 sq. ft. calling for 900 CFM actual or 1350 CFM rated. The Wolf 1500 CFM roof blower would do for this, with an LD-10 Fantech silencer. (I have these). Abbaka also makes a roof blower in this size range, as do Broan.

If you were to use the 60 inch wide model, with about 12.5 sq. ft., you would need 1125 actual CFM from a rated 1700 CFM blower. You might need a Fantech or other supplier in-line blower for this flow rate, or a roof up-blast commercial blower.

While I might imagine that the Wolf and other outdoor hoods are finished to the standard of indoor hoods, I do not know from any experience whether that is true, or even whether they have baffles. Wolf answers their phones, so you can ask.