If your battery is in good shape and just run down from leaving something on (and I'm still amazed that some modern cars from brands that supposedly paid attention to even the smallest details don't have any kind of anti rundown protection) then one of those jump start kits will work, but if you have a battery that is having issues or very cold weather then they are seldom powerful enough. Jumper cables can get you started in those situations.
I've seen jumper cables used to work around a failing started solenoid as well.
Many of the standalone jump start kits have a starting mode where it will use the lower capacity battery to charge a high-discharge capacitor, and then the capacitor actually is used to start the car. This is the same principal as employed by low-current battery charges that have a jump start mode.
Others specify in the instructions that you have to leave them connected for a certain period of time to recharge your primary battery, but this assumes there's any charge capability remaining in your battery.
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