Extract and steeping is just steeping certain grains like color/crystal malts for example,that add flavor but dont need conversion. Partial mash is using extract and mashing some base malts with or without some other malts like color/roasted/crystal malts. Also some malts (mainly base malts) have to be mashed in a partial mash to convert the starch to sugar. As do alot of malts dont need to be in a partial mash but can be "steeped" for extract beers.
Its a pretty easy step from extract/steeping to partial mash because all you need are some base malts and whatever other malts you want with it(even adjucts like flaked wheat/barley). But you should just steep it longer @ about from 147-157 degrees like and hour and rinse the grains with 170 deg water for 10 min(sparge). Also in a partial mash you using alot more grains-particularly the base grains that need conversion and you need to know how much water to use.
So to break it down, your working with more grains in a partial mash compared to extract steeping. Often in a partial mash your using about half maybe of the malts you would in all grain or you can use more or less, your just substituting malt extract for the rest of the batch of your partial mash. So extract/steeping you using almost all extract. Partial mash your using more grains. And all grain, well is all grains.