For example, "Elle est en train de manger toute la pizza". What is the difference between this and "Elle mange toute la pizza"?
There is no difference between those two sentences, as they both describe an action being performed. In this case "en train de" only accentuate that the action is happening right now.
But in a more general way, "en train de" only applies to actions being performed as we speak, whereas use of the present tense (without "en train de") can be used to describe something that is always true.
"Tous les soirs, elle mange de la pizza." translates to "Every evening, she eats pizza." You could not say "Tous les soirs, elle est en train de manger de la pizza.", as she is not eating pizza right now.
I think this is the same difference as in:
- She is eating the whole pizza (elle est en train de manger toute la pizza)
- She eats the whole pizza (elle mange toute la pizza)
Both sentences are corrects with a slightly different meaning. The first sentence indicates that the eating is currently happening, it must happen at the same time the speaker says the sentence.
Note that many English tenses have more than one form, while the corresponding French tense has only one. Thus, for example, depending on the context, the French Present je parle may have for its English equivalent I speak, I am speaking, or I do speak.
Elle sait toutes mes affaires → She knows all my business.
C'est ce que je vous demande→ It is what I'm asking you.
Le moteur ne marche pas → The engine is not working.
Tu crois que je ne sais pas ce qui se passe ? → Do you thing that I don't know what is going on?
In order to convey emphatically in French the Present Continuous (Présent Progressif) one may use turns like
ll est en train de partir. Il est en train de manger.
Note that être en train is a so-called locution figée. You can use it in other tenses as well.
Il était en train de faire les courses quand le taxi est arrivé.