Either is acceptable.

You’ll have to go back and look at the install instructions that came with your hood. My husband’s an electrician and asked for all the documentation prior to doing any work for the appliances. They are all different.

We plug in microwaves with built-in vents and dishwashers; this doesn't look much different.

Most hoods come with cord-and-plug either as an option or as the only way to hook them up. My Jenn-Air only has a plug.

So long as that plug and any cords are not in the air stream then you're likely OK.

Your hood would have come with a plug if that was the way to install mine is hard wired and so was my last vent-a-hood. BTW the pics are really not helpful at all. This is from the install manual for that hood looks like hard wire install to me

1. Install an appropriate 1/2” UL listed electrical wire clamp through the electrical opening on rear of the hood. Install
   electrical wiring from the service panel to the hood location. Consult the connection diagrams (on previous page) for
   further details on electrical placement.

Your hood would have come with a plug if that was the way to install|

Not necessarily. Unless the manufacturer's instructions specifically say that it has to be hardwired, you're free to properly install a cord-and-plug. Same thing happens for dishwashers and garbage disposals. The thing doesn't come with any hook up at all. You either buy a cord or an appliance whip to connect it.