As previously mentioned there IS (a big) difference!
"Bluing" (as we see it today) is really a Black Oxide metal finish now. At times in the past it was once a lustrous blue-black.
It's actually a very fine grained oxidation of the steel's surface (a form of Rust, but not destructive loose red Rust)
Parkerizing is a Phosphate coating that can be different colors (Dark Green through Grey) that's somewhat tougher and less prone to rusting than traditional Bluing.
These days they're also using various Manganese compounds to give matte black coatings that are along the same lines as Parkerizing.
One of the toughest coatings that I've found that can be (easily) done at home is a spray-on coating called "Gun Kote". This is some stuff that I was familiar with from previous activities with competition motorcycles that was called "Kal Gard" and was used as a spray on finish to refinish the Aluminum or Magnesium Side Covers on Moto-X and other Dirt Bikes. It's some really TOUGH stuff!
I've had guns commercially refinished where they first bead blasted them for a non-glare finish, then Parkerized them (more because of the ambient high humidity...to protect the bare metal surface while the pieces awaited their Gun Kote finishing) then finished them with Gun Kote, and given their curing bake.
These guns have made it through 6 and 10 seasons now (2 different guns) and the Gun Kote's still holding up very well. One gun, my 870 Wingmaster, that's been Duck Hunting in the worst conditions for over 6 seasons now is about due to be refinished again. The 10 ga. pump hasn't been out nearly as much and is usually in drier conditions and has seen less wear and is now in its 11th season. It's finish will probably be good for 5 more.
Some of the most beautiful "Bluing" was on commercial firearms, primarily S&Ws and Colts made from the 1880s up to just prior to WW-II. Colt especially used a Bluing process that many call "Carbona Blue" that was done in huge furnaces. I have a book that has photos of the old Colt Factory and these furnaces and racks of gun parts being wheeled into these furnaces where they used bone (meal?) and things like Peach Pits (so I've heard) for their process. Of course incredible buffing was the secret of the bright shiny finish, but the bluing itself was a dark lustrous blue-black that looked like you could see into it 12"...just like a beautiful laquer job on a custom car.:smile:
Even this old Colt made Thompson SMG (the first 15,000 were made by Colt on contract) has "nice" bluing!