>
> What kind of font slants ‘ to the right?
>

Many (but not all) fonts.

>
> Why is that a reasonable rendering?
>

Because the quotation mark is a transformed comma.  The right quotation 
mark is a raised comma, and the left quotation mark is an raised comma 
rotated by 180 degrees.  In many (but not all) fonts, the shape of a comma 
is more or less that of a triangle with an obtuse angle at the top left, 
that is, slanted to the right.  When you rotate such a shape by 180 
degrees, it is again slanted to the right.

>
> And how do you distinguish between ‘ and ’ with that font?
>

Because the thick part (aka the dot) of ‘ is at the bottom of the 
character, and the thick part of ’ is at the top of the character.