Definition:Distinct

Of two or more objects
The same thing as different.

$x$ and $y$ are distinct iff $x \ne y$.

If $x$ and $y$ are distinct, then that means they can be distinguished, or identified as being different from each other.

Or we can say that a distinction can be made between $x$ and $y$.

Of a single object
An element of a particular set of objects is deemed to be distinct if is endowed with a property that the other elements do not possess.

Indistinguishable
Two objects are indistinguishable if they can not (in a particular context) be told apart from each other.

Usually used in the context of physics, in the definition of homogeneity.

So, two objects may be distinct but (at a given level) indistinguishable, like identical twins.

Also see

 * Topologically Distinguishable