The short answer is that infatti may be translated as “in fact,” while in effetti can be translated as “actually,” or “admittedly.” You can get this kind of information from any dictionary. But the question merits a closer look.
Infatti has, over time, become a single word but like many Italian words of this type, started out being two words: in + fatti. It’s extremely similar to the English “in fact,” and, not surprisingly, it means the very same thing.
È quasi una sorella, anzi è una sorella. Infatti, parliamo allo stesso modo... e facciamo le stesse cose.
She's almost a sister, or rather, she is a sister. In fact, we talk the same way... and do the same things.
Captions 4-6, Amiche - sulla spiaggiaPlay Caption
The fact is, both infatti and difatti come from the Latin de facto (from the fact) which is also used in English to mean that something exists in fact, although perhaps not in an intentional, legal, or accepted way: de facto. The direct Italian translation of the Latinde facto is di fatto—two words, like the Latin. Note that this term uses the singular ending, as in the Latin.
When we go to a meeting, and it doesn’t actually take place for some reason, we can say it was nulla di fatto (nothing actually happened).
In the following example from the very first episode of Commissario Manara, introductions are being made at police headquarters. Pio, meaning pious, is an old-fashioned but common enough name in Italian. Buttafuoco’s co-worker is making a pun, saying Pio Buttafuoco is a good and maybe even religious person.
Buttafuoco. -È pio, eh di, di nome e di fatto.
Buttafuoco. -He's Pio [pious], uh in, in name and in fact.Play Caption
Unlike infatti, in effetti is made up of two words, and though, like infatti and difatti, it comes from the Latin de facto, it’s a bit more subjective, and has to do with taking something into consideration and admitting that, “yes, that is actually so.”
In the following example, in effetti is used because one couple realizes that they have actually been absent for a good while, and so the question is more than justified.
Ma è un po' che non vi si vede. Dove siete stati? Beh sì, in effetti siamo appena rientrati dall'India.
Well, it's been awhile since we've seen you. Where have you been? Well yes, actually we've just gotten back from India.
Captions 7-8, Escursione - Un picnic in campagna - Part 4Play Caption
In this case, they could just as easily have said:
Beh si, infatti, siamo appena rientrati dall’India.
Well yes, in fact, we just got back from India.
It’s just a different slant, like saying “in fact” instead of “actually” or “as a matter of fact.”
In effetti can be used when you’re forced to agree with someone, but not all that willingly, or when they have convinced you of something.
You might say:
In effetti... hai ragione.
Admittedly... you’re right.
The other person who knew he was right all along, and was waiting for you to realize it, might say:
Infatti, ho ragione!
In fact, I am right!
He might also just say:
Infatti can be used by itself to confirm what someone has said. You’re agreeing wholeheartedly. It may not actually have to do with facts, but is used in the same circumstances in which we use “in fact,” “as a matter of fact,” “that’s a fact,” or “that’s true” in English. It’s usually expressed with an affirmative tone.
In effetti is more like a consideration. It’s more like “admittedly” or “actually.” The tone may well be one of realizing something you hadn’t considered before. You might raise your eyebrows. The adverb form of in effetti is effettivamente and can be used interchangeably for the most part.
To sum up, there are definite differences in the words discussed in this lesson, but the differences are, in effetti, fairly subtle, and so you have to pay close attention to really grasp them. For the most part, if you stick to infatti to be emphatic, and in effetti to be a bit more thoughtful, you’ll probably do fine! Listen to the tone and context in the Yabla videos to get more insight into these words.