Differences between basic, complex and terminological facts in a Knowledge Base using First-Order Logic
In &sect;3.2 they distinguish between the following four grammatical categories, with some examples:


Predicates: Woman, Rich, Beautiful, Bankrupt
Relations: LivesAt, HadAnAffairWith, Loves
Functions: fatherOf, bestFriendOf, ceoOf
Individual constants: maryJones, johnQSmith, tomsHouse


In the background they have first-order logic with identity, which means they allow for quantification only over individual variables. Within this machinery, in &sect;&sect; 3.3&ndash;5 they introduce the three types of facts.


  Basic facts are the atomic sentences and their negations.


The atomic sentences are those sentences which are made of: 


a [predicate] + an [individual]. E.g.: Woman(maryJones)
an n-ary [relation] + n [individual]s. E.g.: Loves(maryJones, tomsHouse)
an [individual] + "=" + an [individual]. E.g.: maryJones = marySmith


Note that functions applied to individual constants also denote individuals (e.g., fatherOf(maryJones) is some individual), that's why clauses (1&ndash;3) include the word 'individual' rather than 'individual constant' so as to allow also for functional expressions denoting individuals. The negations of atomic sentences are defined as follows: a sentence &not;S is a negation of an atomic sentence iff S is an atomic sentence.


  Complex facts are the basic facts closed under boolean connectives and quantifiers.


That's just a fancy way of saying that: (i) basic facts are complex facts, and (ii) if &phi; and &psi; are complex facts, then &not;&phi;, (&phi; &and; &psi;), (&phi; &or; &psi;), (&phi; &rarr; &psi;), and &forall;x&phi; are also complex facts. They give the following example of a complex fact on p. 34: &forall;y[Rich(y) &and; Man(y) &rarr; Loves(y, jane)] (every rich man loves Jane).

Beware that on p. 36 they list sentences like "jane &not;= john" among complex facts, suggesting that they're not basic facts. But they are. I suspect that's why you've been having hard time seeing the difference between the types. By the definition of basic facts (see above), sentences like "jane &not;= john" are considered basic, because they're the negations of atomic sentences such as "jane = john". 


  Terminological facts are complex facts taken to be axiomatically or definitionally true.


A better term for them would be "definitional facts" or "meaning postulates" (as Rudolf Carnap calls them). Consider the predicate Man. If someone is a man, we know, without having to see this person, that he is not a woman; it's definitionally true! We capture that logical relationship between predicates Man and Woman with the terminological fact: &forall;x[Man(x) &rarr; &not;Woman(x)]. That is only one example of a terminological fact; more can be found on pages 36&ndash;7. They're pretty straightforward to understand.

Hope this helps clarify the distinction.