"Maintaining" is discarding and feeding your starter on a regular weekly schedule, always maintaining 1:1:1 ratio of starter to water to flour, to ensure the continuance of its strength and health, while keeping it in your refrigerator until you are ready to bake. When you are ready to bake bread, there are several methods of preparing your starter for that process. (Below is one that produces a very large hole filled crumb).
“Feeding” is adding equal parts flour and water to the starter, after separating the amount you are trying to maintain, and discarding the rest. (Typically discard 2/3 of the original starter). For a starter's yeast and bacteria to continue to grow in strength and peak time, it needs to be fed at least the same amount each of flour and water as the starter you are feeding. For example, I recommend discarding to 60 grams of starter every time, so I know that I will be adding 60grams of water and 60grams of flour to the starter that I am feeding. Easy number to remember. (You can add more than that as long as the flour and water amounts are equal to each other, and at least the same or more than the quantity of starter). This will give you 180grams of starter to maintain. You can actually maintain a smaller quantity, down to say 60 grams total, (20g each starter, flour, water) with this weekly method.
“Discard” is the starter that is removed from the original starter to make room for the "feed". It helps to keep the total starter quantity at a manageable amount. It is typically quite a bit since it is usually 2/3 of the previous amount. (This amount will vary based on how hungry you let your starter get, so always weigh out to the amount you want to keep not the amount you are discarding!) Basically discard, is starter that is not freshly fed. You can throw it out; you can collect it in a freezer bag kept in the freezer so you can use it later in discard recipes; or you can feed it for a second starter, to share with someone. If you have a lot, it needs to be refrigerated and must be used within 1 week unless you add more discard to it, or feed it to use. (Keep in mind that this discard has not been fed since your last feed, so if its been a week since then, it is going to be breaking down which is why it is only usable for another single week before it turns into unusable alcohol, unless you do add to it). I actually collect discard until I have enough for a recipe. Sometimes I will feed the discard a small amount of flour and water to prolong the useable time frame, or because I need more discard for a recipe. You need to add instant yeast to discarded starter to make bread because it has stopped growing, and thus, wont be able to leaven bread.
“Prepping” the starter is repeating the feeding process several times in a short period of time, over 1-3 days, with higher ratios of flour and water to increase the speed and strength of the activity of the starter for actual leavening. (Usually only a small amount that is bulked up with the process, not feeding all of the main starter that you are trying to maintain). There is an aggressive prep schedule on the maintaining starters page.
"Levain" the pre-ferment. A specific amount of starter that is freshly fed and left to activate to a bubbly state to make bread, usually done the morning of baking.
"Autolyse" is the water and flour of a bread recipe mixed together and left to rest for a few hours before mixing with the "levain", then salt, to make sourdough bread dough.
"Bulk Ferment" is the resting time, usually 4 to 10 hours, at a warm temperature, for the bread to rise and ferment its sour flavor. The time varies by temperature of the dough which determines how much rise you need to have before the "cold retard", or "Cold Ferment".
"Cold Ferment" or "Cold Retard" is the time that the dough is in the refrigerator to stop its rise and further its fermentation, or sour development. This is anywhere from 8 to 36 hours depending on your recipe and desired results. This also provides an easier surface for scoring, as well as helping with the spring open of the dough during baking.