Ideal and non ideal diodes
They are both just two different ways of saying that you don't need to worry about the variation of voltage across the diode as a function of the current through that diode. Whether or not you assume \$V_D=0\:\textrm{V}\$ or \$V_D=700\:\textrm{mV}\$, doesn't really matter. (One might be said to be "more ideal" than the other, but that's moot.)

So in one case the author is saying that the diode is not ideal in the sense that \$V_D=700\:\textrm{mV}\$ but implying that it is still ideal in the sense that \$V_D\$ doesn't vary with current (implied.) The other author is taking note of the fact that \$V_D\$ doesn't vary with current (now made explicit), so it is "ideal" in that sense, while taking note that they want you to use \$V_D=700\:\textrm{mV}\$, anyway.