The Jetpack is a piece of equipment that is equipped in the breastplate armor slot. It has no armor, but it allows the user to fly in the air. Flight is quite different than in Creative mode. Fly into the air using the JUMP key, but look out, as the Jetpack will not negate fall damage. Also note that you maintain your ground speed while flying, so if you sprint and/or use a swiftness potion before you take off, you will continue travelling at that increased speed while flying.
When you press the JUMP key and M key while flying, the Jetpack will switch into "Hover Mode", where it will then fly upwards much slower and gradually descend. This functionality is also included in the Electric Jetpack. The Hover Mode uses less energy than regular flying. You cannot fly upwards, but you can slowly descend. Turn Hover mode off again to fly up.
The jetpack can use Biofuel Cells, Coalfuel Cells, and Fuel as sources of power. If you wish to use either Cell, you must recharge the jetpack with a Canning Machine. 18 Biofuel Cells or 6 Coalfuel cells will charge the jetpack to about 90% full capacity. If filled with Coalfuel, the jetpack will last slightly longer, but both types of cell last about 55-60 seconds.
To power the jetpack with Fuel, you will need a Jetpack Fueller. The jetpack can be anywhere in your inventory, including on your back, and hold the Fueller in your hand. Right click on a Tank with Fuel in it, and your jetpack will be instantly completely refilled, using ~1/4 of a bucket of fuel. Note that it cannot be powered with Oil.
NOTE: The Jetpack Fueller has been removed from the current version of Technic
When compared to an Electric Jetpack... well, there really isn't a comparison. First off, to refuel the Jetpack, you need Bio or Coal fuel cells, both of which are complicated and time consuming to create, requiring many complex machines, as well as a Canning machine to finally even use them to charge the Jetpack. In comparison, all the Electric Jetpack needs is some form of electricity. It can be charged by Single Use Batteries, RE Batteries, a Batbox, Charging station, etc.
Second, the Electric Jetpack is only slightly more difficult to craft. It requires a total of 4 glowstone dust, 2 lapis lazuli, 2 more redstone dust, 5 more Tin Ingots, 4 more copper cables (4 rubber, 2 copper), and 5 wooden planks making it cost 4370 EMC with what ever your rubber costs are. That's not a whole lot more than the standard Jetpack, yet for that bit more, you get almost four times the flight length and much easier charging. The Electric Jetpack lasts about 3:30 non-stop flight with Hover Mode off. You can imagine how long it'd last while using Hover Mode.
That's another difference: With the standard Jetpack, the Hover mode simply goes down slowly, even if you hold jump. With the Electric Jetpack and Hover Mode on, you'll actually rise slowly if you hold jump, and drop slowly if you let go. This makes it much less awkward to control, since you don't have to keep switching modes to go up and down.
Really the only thing the Standard Jetpack has over the Electric Jetpack is the height limit. In the Overworld, the Electric Jetpack will go up to 185 and only up to block 85 in the Nether. The Jetpack will go up to the world height limit in both worlds.