Are there differences when working with light-colored palm sugar versus dark? Depending where I get my palm sugar from, it's either light brown colored and quite hard (pictured left), or a very dark brown color and much softer (on the right). 

 

Are these different types of palm sugar? I sometimes note the one on the right is called coconut palm sugar and comes from Singapore. The one on the left looks Vietnamese.

Are either suitable for recipes calling simply for palm sugar?
The pale-colored disks of palm sugar have a mild taste, and can be used for any recipe which calls for palm sugar, or for that matter light brown sugar.  It's that not strongly distinct from granulated sugar in flavor; personally, the only reason I use it is for texture.

The dark brown palm sugar has a distinct caramelized, even somewhat burnt flavor.  It adds considerable, distinct, flavor to a dish, even a heavily spiced one.  You should use it in dishes which are specifically supposed to have a palm sugar flavor, but should be careful using it in recipes which say things like "Palm sugar or granulated sugar".

It's really like brown sugar vs. molasses.  Sometimes you can substitute them, but not always.

There are probably also ethnic differences in which one you want to use for what, but I don't have enough experience of Southeast Asian cuisines to tell you that.