I'm looking at a few models of computers from Dell and HP that I'll be using to edit and render video using Vegas Pro 20. Each manufacturer has everyday desktops, but also so-called "work" and "gaming" desktops. Is there any real difference or is this all just marketing hype?
Compare the components and cases. What's different?
A more informative and less condescending answer would be more helpful and appreciated.
Nobody is being condescending here. If you came back with information about the components and models you are considering you'd get proper advice.
Dell and HP have huge product lines ranging from workstations to budget builds for offices to gaming and casual home use. Prices vary by thousands of dollars. Yes there are differences- which ones are you comparing?
The case is also important for airflow- see poor reviews of Alienware cases in past years which limited the performance of otherwise high-end components. 
@Dave-B Not looking at any particular brands, as I always build my own desktop; I would choose "game" for using Vegas pro if you have to choose a pre-build desktop between advertised "game" vs "work". The thing is, high end gaming requirements are not that different from editing and rendering, and surely require more capable hardware than desktops designed for "work". "Work" desktops are optimized for office applications, running silent, are cost optimized and energy efficient.
I am happy with the performance of my own build; see my signature.
I second what @bitman and @RogerS wrote. My computer specs are in my signature. I don't (and haven't for decades) bought a pre-built. The reason for me building the computer myself is that if I want to upgrade it, I can do it easily. With the same motherboard I have, which originally had an AMD Ryzen 9 3900X and RX480, is now with a Ryzen 9 5950X and RX 6700XT, for the cost of just buying the parts, not a new computer. Also, I have a case that has airflow. Phanteks P400A, in addition to a Thermalright Peerless Assassin CPU Cooler. All this helps the computer run cooler and faster.
A gaming computer works great with video editing, but a computer you have to consider the compute as a whole.
For what it's worth my own recent build is here. I did look at prebuilt machines (including Dell) but for the price and with concern about questionable OEM design choices decided to learn how to put one together.
The only thing I'd change on it is getting a somewhat smaller power supply as I sized it thinking GPU power use would grow more than it has (RTX 40XX is more efficient than the 30XX were). The case is also on the large side but airflow is excellent.
Just out of curiosity, I've recently been having a look at the new desktops from Dell (Australia). One thing that I've noticed is that Dell's XPS desktops do not an HDMI output - there's only a DisplayPort video output. While Alienware models do seem to have an HDMI output on the GPU card, but it's not mentioned on Dell's 'Ports and Slots' listing. Also with new Alienware desktops, there's only one HDD slot by the looks of it whereas my 2.5 years old Alienware desktop has 1 x 3.5" and 2 x 2.5" HDD slots.