Tap controls means that the settings are stepped. You cannot set up a heat range or wire speed between those steps. This can be a problem. Continuous means that you have infinite adjustment.
As for cheap vs. expensive, you will learn to curse new phrases if you buy a cheap welder. It would make more sense to buy a name-brand, higher-end welder (at least one of the higher-end 110 machines) and then sell it when you are done. A new Lincoln 135SP with a tank will set you back around $600. On the other hand, you would spend that on labor to have floor pans put in, easy.
OK....unsolicited commentary aimed at no one in particular. A lot of guys want to go cheap on tools. For some stuff, this is fine; for other stuff, this is not good. Body panel welding is critical...if you screw up, your car will look not so good. Good panel welding is hard enough with a good welder. On the other hand, I've bought an assortment of die grinders from HF...cheap. They do the trick and have held up well. Other stuff from there isn't worth the money I spent to go pick it up from the store! Remember, these are $30K cars, at a minimum, if you do it right. You cats with '70 or '71 models are looking at even bigger money. What's a few bucks more for tools?