Need help with rear axle identification.

So I'm trying to figure out what rear axle I have so I can get new gears.  Truck is a 1983 F250 4×4 long bed single rear wheel.  Axle code is 33, which depending on the site gives me different answers.  The chart here just says Dana, but not which one.  The axle does have reverse thread studs on the driver side.  Its not a full floater from what I can tell.  

Looks like a semi-floating Dana 60.
There should be a "60" cast into the diff housing web at about 4 o'clock. You can get more specifics if you're able to find the BOM number stamped into the passenger side axle tube (format is: xxxxxx-x). With the BOM number, you can go to a number of places (including here) to look it up.

Thanks, I'll see if I can hunt that down.  

You need to replace the vent tube that should be attached to the bolt holding the brake hose splitter to the axle housing.

Not having one can allow water to enter, and if the hollow bolt gets clogged your axle will force gear oil into the brake drums when it warms up in use.

It looks like you have a build tag attached on the left side of the diff cover, but it's hard to tell on my phone.

Do you have a picture of what the vent tube should look like?

I could go take a picture, but a bit of searching around finds these.
The first, how the vent hose comes off the vent bolt and goes up the left frame rail.
And in the second Cory shows where the top of the hose attaches to the upper frame rail flange (asking where the broken hose attaches at the bottom)

OK, so, two ways here.

First, in the attached picture, there's a plate on the left side of the diff that is mounted across the two bolts on the side. That is your ID tag and has all the info. If you need to clean it off, use a stiff nylon or brass brush, steel will scratch it up and make it hard to read.

If you can't read it, you can clean off the gunk in the area with the blue circle and that will have a Bill of Materials number (BOM) stamped on the axle tube and you can find your listing here:

https://www.axlebuilder.com/dana_60_bom.html

Either way you will get axle type/model, axle splines, gear ratio and limited-slip/open differential.

You folks are fantastic, thanks for all the help.

Easy! Only Dana axles were used though the 1984 model year, and a model 60 is the only one to have semi floating axles.