I used to maintain 3 starters:
A stiff wheat starter, with the flour blend as used by the late French baker Gerard Rubaud (70% bread flour, 18% 50-50 blend of hard red winter and spring wheats), 9% spelt and 3% rye. I followed his methods explicitly, which included always refreshing the starter at peak - which meant, 24/7, every 5 hours at 28C, religiously. You got that right - woke up in the middle of the night to refresh a stiff starter.
A liquid rye starter. It has been my main starter for a long time, for any kind of bread regardless of the grains or flours. I use Central Milling's Type 85 flour, with 0.85% ash. It corresponds to a French T85, or a German T 850 if they had it (the Germans don't have an equivalent - the closest wheat they use with this ash content would be a T 1050, with 1.05% ash).
Lievito madre.
I used to refresh the rye, my only starter for a long time, about once per week. Now, with the LM, I do both usually at least 3x/week because although it will survive, a weekly schedule of the LM refreshment would significantly acidify the LM and defeat it's purpose, a mild, wild-yeast centric stiff starter.
As to the discard, I don't really use the LM discard but I do save the rye discard and make fleur de levain - adding it from time to time as a flavoring component. Because it's spread out thinly and dried in the oven at about 200F for 90 minutes or so, it is no longer leavening. I grind the flakes into a powder and freeze it for later use at about 1 tbsp/1 KG dough.