Yesterday I checked my rear differential fluid and it was very low so I filled it up and plugged it back up. Started it up and drove it home with no problems. Got in it today and drove to the nearest corner store and back, no problems. Jumped in it again and jumped on the highway for less than 5 minutes...I had my foot down on the gas pedal and let off the gas. But when I put my foot back down to speed up, my rpms jumped to 4,000 and it was barely pulling so I continued to drive it to the nearest exit, the whole time I seen smoke and smelt transmission fluid. Pulled it in an empty lot and got out with the engine running and looked under the truck. Transmission fluid was dripping everywhere, but looked as if it was coming more from the transfer case. There was a hose that was disconnected from the top of the transmission, but I don't know what the other end is attached to.

So, now I'm puzzled. Did my rear differential go out ? Or did the disconnected hose cause this ? Or did my transmission fail on me ??

 

Just to properly identify things:

Engine - automatic/manual transmission - transfer case - rear axle differential / 4x4 to front axle differential - to wheels.

Lets work our way through the components:

ENGINE TO TRANSMISSION
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Engine is connected to the transmission via (torque converter in an automatic transmission) or (clutch in a manual transmission).

After the rear end of the engine follows in either case about 2 feet of transmission.

TRANSMISSION TO TRANSFER CASE
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Normally the Blazers do have a transfer case. In any case all 4x4 models do. Not sure about the 2WD, I think that one would have an extension on the transmission case.
The transfer case is just about 1 foot long and located, actually flanged together with the transmission and just about above the crossmember on the frame visible on your video. I don't know but think there is no vent on the transfer case. If it is a 4x4 you will have the drive shaft exiting the left hand side of the transfer case to the front axle, while the main drive shaft exits along the vehicle axis to the rear axle.

The transfer case should have a drain and filler plug. Normally just filled to the filler plug until oil starts to drip back out. Special oil is normally required. Gearbox stuff.

DIFFERENTIAL either REAR OR FRONT
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On the S10 normally the front differential ("diff" for short) is offset to the left between the front frame members as the drive shaft from the transfer case passes the engine on the left hand side somewhere under the steering.

Rear Axle Differential is located between the wheels on the axle and serves the dual purpose of distributing the longitudinal input from the driveshaft across to the wheels and at the same time allows for different number of revolutions on inside or exterior wheels when turning. (exeption = limited slip differential)

Normally a differential is just filled to the filler plug height with a rather sticky gearbox or hypoid oil. (special stuff - the pinion and ring gear are subject to very high pressures on the flanks).

Not sure about the later years my 1994 still has a vent hose on the differentials into the highest parts of the frame at the rear diff.


YOUR PROBLEM
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I hope it is just a broken line. If rpm rises without anything happening it could (let's hope for the best) just have spilled the transmission oil and gone limp. No oil and the torque converter is no longer able to transfer the engine rpm to the transmission. Oil in the transmission is pumped by a pump contained within the transmission in order to have hydraulic pressure to open and close the various clutches. So if you have a leak in a line it spills quickly.

I'd suggest to first identify the leak. Broken line could (and I say could) be an easy fix.

BTW - How did you fill up the oil, where and to which level?