With sforzo, we have an S at the beginning of a word once again, and we might recognize the word without the S as looking like the noun forza. In fact, forza vs sforzo can cause confusion for non-native speakers of Italian, because they are both about strength, in a way.
In the popular detective series on Yabla, Imma Tatarannni is trying to get some information from the young woman whose boyfriend was murdered. She uses the noun sforzo as she talks to Milena.
Allora, Milena, ascoltami. Ora tu devi fare un piccolo sforzo, va bene?
So, Milena, listen to me. Now, you have to make a little effort, all right?Play Caption
We have translated Imma's use of sforzo with "to make an effort" but we might more likely say, "Now you have to try a bit harder." "Now you have to really try."
We have seen that an S at the beginning of an existing word will often change it to an opposite meaning, but it can also reinforce it, and that is basically what is happening in the example above (although this is even clearer when looking at the verb forms forzare and sforzare as we do below).
When you make an effort, you use some reserves of strength. The noun la forza is "the strength" or "the force" (easy cognate!). It's actually a very popular word, so see our lesson all about forza. It's a great noun to know because it's used so much, especially in conversation.
Sometimes it's hard to remember that lo sforzo is a masculine noun and la forza is a feminine noun so let's keep in mind that lo sforzo is "the effort," and la forza is "the strength."
The noun la forza is easy to understand, as it is a cognate of "the force," but is often translated as "the strength."
One example of this noun is the subtitle of a popular biopic about Adriano Olivetti, the man behind the well-known Olivetti typewriter. Adriano Olivetti - La forza di un sogno (the strength of a dream).
Both lo sforzo and la forza are associated with verbs: sforzare and forzare. Sometimes these two verbs mean the same thing, but sometimes we need to distinguish them and that's where it can get tricky. Which to use?
E mi prometti di stare tranquilla, di riposarti e di non sforzare il piede?
And promise me you'll stay calm, rest and not strain your foot?
Captions 1-2, Sposami EP 3 - Part 2Play Caption
In this case, we're talking about putting too much pressure on the injured foot. Some people might use the verb forzare to mean the exact same thing, as sometimes forzare means going too far.
In the following example, sforzare is used reflexively to mean "to make an effort," "to try hard."
Piggeldy si sforzò di camminare come si deve.
Piggeldy made an effort to walk properly.
Caption 14, Piggeldy e Federico Il cieloPlay Caption
Sometimes forzare means "to use force" as implied in the following example.
Eh, qualcuno ha forzato i cancelli del canile comunale, sono scappati tutti i cani,
Uh, someone pried open the gates of the town dog pound, all the dogs escaped,
Captions 68-69, Il Commissario Manara S1EP8 - Morte di un buttero - Part 3Play Caption
Of course, as with many verbs, the past participle of forzare may be used as an adjective, and often is. Sforzare, on the other hand, isn't commonly used this way.
La prima settimana di libertà dopo mesi di confino forzato!
The first week of freedom after months of forced confinement!Play Caption
When your car gets towed from a no-parking zone, in Italy, it's often called rimozione forzata. This is because they will remove the car without having to ask you. You want to avoid parking in these areas, so these might be a good couple of words to know! To see what these signs look like, here's a link.
As to when to use one or the other verb, don't worry about it too much, as sometimes it depends on personal preference. It's more important to remember about the noun, as we have mentioned above. Also, keep your ears open to notice which word people use in various situations.
P.S. The use of S as a sort of prefix in Italian comes from the Latin prefix "ex!"
P.P.S. Sforza (with an "a" at the end) is not a noun, at least not a normal, common noun. It is used as a proper noun — as a family name, and in particular, it was the name of a Milanese ruling family in the Renaissance, and a power name at that.