In comments, John Lawler answered:
Thinking is a present participle; that's the form of the verb that's used in the progressive construction. Eating could be a noun or it could be a gerund in I was thinking about eating -- the speaker would probly know, and might make it obvious in speech, but a reader can't tell. Add a direct object, though, and eating is unambiguously a verb, hence a gerund. Add a definite article, and it's a noun: I was thinking about the eating (not the drinking). Without the context, one can't tell.
In the gerund clause
X's eating the apple, eating is the gerund. But without a direct object, it's not possible to tell whether it's a gerund or not. Let me say that again -- with only an -ing verb as the object, it may be a gerund or it may not be. Schrödinger's gerund, if you like. It's not automatically to be thought of as a gerund just because it ends in ing.