Yeast will change it's fermentation characteristics and taste on multiple factors.
Shape of the vessel,
Open vs close vessel,
Depth of the vessel.
Temperature of fermentation.
I use the same yeast all the time.
if I want to get lager (clean) characteristics I pitch more yeast and ferment cooler.
If I want to get more ale (eatery) characteristics I pitch less yeast and ferment warmer.
It is all about the taste and not about definition in my opinion. Grab a yeast strain that can do both, learn it and use it to your advantage.
To me, the perfect yeast strain for this is Wy2124 (Saflager 34/70). Good points everyone. Not sure about the true Scotsman point, but alright!
I think what makes a lager a lager is the yeast. It's what makes a Trappist a Trappist, a Belgian Strong a Belgian strong, a hefeweizen a hefeweizen, is it not? You wouldn't use a neutral ale yeast in a hefe wort and call it a hefe? Well, I suppose you could, but it sure wouldn't taste the same. Maybe it's a little more subtle with lagers vs clean ale yeast, but still, I think you see what I'm getting at...
EDIT: dang it, my post went in just shy of 10:56. Such a magical time, isn't it?