Laptop power supplies - why the spectrum of voltages and connectors?
There are multiple reasons that all come into play when dealing with the power requirements of a new laptop design. The main goals are to have the longest battery on/standby time possible while still being light, small, reliable/resilient, and quick to charge.

The battery must be able to provide enough power for the laptop to be on for a couple hours. This power requirement varies from laptop to laptop based on how much power the device uses. Here are the battery and power supply specs of a few laptops I have laying around.


Small Sony laptop that has a 7.4volt 7800mAh battery that provides the laptop with about 58 watt hours of power. Since this laptop is small and doesn't use much power, it will last a decent amount of time, but also because it's small, the battery is much smaller and lighter than other laptop batteries. The power supply provides 16volts 4amps.
Big ~2005 Toshiba that has a 10.8volt 3900mAh battery that provides about 42 watt hours. The power supply provides 15volts 5amps.
Average size ~2006 Compaq that has a 14.8volt 3600mAh battery that provides about 53 watt hours. The power supply provides 19volts 3.16amps.


Now because the batteries have different voltages, capacities, and technologies they need to be charged differently. This is where the different power supplies come in, they need to be able to power the laptop, and be able to charge the battery at the same time, without damaging or overcharging it. You can destroy some batteries, even causing fires or worse by charging them with the wrong type of charger. Take a look at Battery Chargers and Charging Methods for more information. I think most laptop batteries are lithium-ion, but I don't know that for sure. 

So for some charges, there is a lot more to do than just providing 12volts with up to a few amps. Depending on the laptop design, the battery charging circuit (the circuit that prevents the battery from overcharging or being charged too fast, etc.) may be located inside the laptop itself or in the charging unit. If the only thing the power supply does is to provide a voltage around 12 volts, then you may be able to run it off your car cigarette lighter. But I would not recommend this since the voltage will vary greatly. Vehicles, especially older ones, do not provide a constant 12volts. As for the amperage, a cigarette lighter should provide more than enough amperage, and if not you would most likely just blow an accessory fuse. However if you laptop's current power supply is around 9volts or less, you could probably rig up a DC to DC power regulator to provide that voltage from the vehicle.

As for the plug that they use to connect to the laptop, for the most part it doesn't matter. Sometimes chargers provide multiple voltages, and/or have feedback that requires more than two conductors but for the most part they only need 2. The plug you referenced in your question, "yellow tip EIAJ-04 power jack," is just a generic coaxial plug that provides two conductors (inner and outer) It is used by some different laptops. But a reason that they all don't use the same plug is so that you can't hurt your laptop by pulling in the wrong adapter, and I'm sure there is a bit of hope that if your power supply gets broken or lost that you will buy another one from them since it may be hard to get a generic one.

Keep in mind that the plug its self is not really important, it's the power supply that connects via the plug that matters.