Differences between starters

No, my preference is to just maintain one rye starter with which I can build preferments to make anything else. Occasionally if I know I am going to bake a few white loaves I will maintain a white starter alongside the rye starter but only for convenience.

With a rye starter I can make either a 100% rye preferment for use in rye loaves (pumpernickle style) by adding more rye flour and water, or I can make a white preferment by starting with a tiny amount of the rye (say 10-15g) and then adding white flour and water to build it up to the required amount for my recipe. By the time that amount is reached the 10-15g of rye in it are miniscule and make no difference to the look or taste. In the same way you could build a preferment with any other flour using the tiny amount of rye starter to innoculate the larger mass.

I maintain the rye starter in preference to a white starter because I find rye to be the most active in terms of wild yeasts and it's easy to maintain.

To expand your original question a little, if we talk about preferments rather than mother starters then most definitely, different preferments/levains have different textures and tastes. If you put say 150g of rye starter into a loaf made with white flour you will certainly notice the colour taint and the nuttier taste. It's really much the same as just mixing different flours in the main dough itself. The tastes attributable to the starters themselves come from the yeasts and labs in the mix which create the mild-to-sour flavours associated with starters.

I second ElPanadero’s response.  I used to keep only a stiff whole wheat starter, now I keep only a liquid rye starter.  Both have worked for all kinds of bread.  I suppose if one were a pro baker making large quantities of very different breads everyday it would make sense to keep multiple starters, but as a once a week home baker I don’t see much advantage there – with a few feedings I can have any kind of starter I want from one week to the next.

Marcus

I keep one white starter and convert it to rye, ww, etc. as needed in a 2 -3 step build.  No need to keep multiple starters except if you want to keep a Yeast Water one as well.

Partly because I can do everything I need to do with just the one, but also largely because I'm not so great at maintaining things on a regular basis! I have my beautiful lively little rye sour, and it more or less maintains itself because I bake a loaf of deli rye almost every week, so I don't have to be reminding myself to feed it - the three-stage build takes care of that. It lives in the fridge between bakes, and it seems exuberantly happy with every outing. When I need starter for something else I use a very small amount of the sour as a seed and I build from there, and it works beautifully - I haven't yet encountered a situation that required a special-purpose starter of some other kind. If it ain't broke, I don't fix it.

I keep a stiff 50-50 ap-ww starter @ 60% hydration. I the build to ww in one feed or rye in 3ish feeds.

I keep a single 100% hydration starter, it's "kinda" fed with white flour, it's been fed a high-extraction type 70 flour from central milling for a few years now, but before that it was a white starter.

I keep it this way because that is how it had always been fed previously (came from a family friend).  At the height of my insanity, I kept the one I currently have (Bill), a stiff starter that I first begin propigating in my home town (Osos), and another 100% hydration one that was only fed a mix of barley/rye/whole wheat (Grainy).  I dropped the latter two because I just don't bake enough bread to keep them up.

Do you maintain (using identical steps) more than one starter because they taste or behave differently?

I maintain only one starter unless I am experimenting (i.e. trying to change my original starter). I would say the max number of starters to maintain that still make sense for you, should be based on your sourdough starter keeping skill, baking skill and especially baking frequency:

new: 1 starter is enough, focus on that one first. Bring it up, maintain it to your desires.

familiar: 2 starters should be ok but it's based on your baking. I recommend one maintained as stiff and one as liquid starter. Why? Because lactobacillus thrive in liquid medium so if you wanted a sour loaf you would do a stiff dough from a liquid starter. Read Debra Wink's explanations if it doesn't make sense just yet. :) Stiff starter, on the other hand, is great for raising power and milder tasting bread.

expert: someone really experienced at baking could use different starter mixes to get more exotic flavours but I think that's really professional's domain.

It all depends on how often you bake too. If you bake every 10 days or so then maintaining more than 1 starter is counter-productive because you can just build a new one like others have said. But if you bake every (other) day or so then maintaining more starters is easier because you need them to be "ready" so often. Whatever is easier for you.