There are two basic words for "wild" in Italian, and they're sometimes interchangeable and sometimes not. They're also rather similar in that the root is the same: selva (woods, forest).

One of the adjectives for "wild" is selvatico (wild, uncultivated, growing spontaneously, feral).

Sto cercando di renderla un po' meno selvatica

I'm trying to make it a little less wild,

e un pochettino più civile.

and a tiny bit more civilized.

Caption 27, Gianni si racconta - L'olivo e i rovi

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When there are two varieties of a plant such as finocchio (fennel), the wild one gets qualified with an adjective: finocchio selvatico.

Il Monte Pellegrino ospita centinaia di specie diverse di piante.

Monte Pellegrino hosts hundreds of different plant species.

Dal cipresso al pino, ci sono numerose pinete,

From cypress to pine, there are a number of pinewoods,

agli alberi di fico d'india, ai gelsomini, al finocchio selvatico,

to prickly pear, to jasmines, to wild fennel,

che da una sensazione di freschezza all'ambiente.

which gives a sense of freshness to the place.

Captions 25-28, Adriano - Monte Pellegrino

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BANNER PLACEHOLDER

Sometimes wild fennel is called finocchietto (becoming an altered noun, by means of the diminuitive suffix -etto) because the plant has a smaller bulb, and is of "minor" importance. Other times, though redundant, the wild kind of fennel is called finocchietto selvatico. This pianta spontanea (spontaneous, or wild plant) is an ingredient in many central and southern Italian preparations, from salame to minestre (soups), to castagne lesse (boiled chestnuts). It blooms in late summer, and if you wonder what part people use, well, they might tell you, "whatever part is on hand when you want to make your dish." The seeds are tasty right off the plant, but they can also be dried and boiled to make a refreshing and aromatic hot tea that aids digestion. It's one of those plants that's worked itself into a great many recipes, both humble and otherwise, because, in addition to being aromatico (aromatic) and gustoso (tasty), it grows just about everywhere, and is free for the picking! The bulb (the white part) of cultivated fennel is eaten raw in salads, in pinzimonio, or cooked in a variety of ways.

The other word  for "wild" is the adjective selvaggio, especially referring to unrestrained people or savage animals, or places that have no law, or terrains that are particularly difficult to navigate.

Selvaggio can also be used as a noun, as in the following example.

Rapiti dal fascino dell'eterno selvaggio,

Captivated by the appeal of the eternal wild,

narrando delle culture con cui venivano a contatto.

telling of cultures with whom they came into contact.

Captions 4-5, Linea Blu - Le Eolie

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When referring to meat from hunted animals, for example cinghiale (wild boar), we use the term selvaggina (game), also called cacciagione (hunted meat).

Tavole imbandite senza posate, com'era uso,

Tables decked without silverware, as was the custom,

e con i cibi dei ricchi e dei nobili.

and with the food of the rich and the noble.

Paste reali fatte di pasta di mandorle,

Royal pastries made with almond paste,

anatre all'arancia,

ducks with orange sauce,

maialini farciti con spezie e molta selvaggina.

suckling pigs stuffed with spices and lots of wild game.

Captions 13-18, Linea Blu - Sicilia

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BANNER PLACEHOLDER

In a nutshell:

When you think about wild beasts, or when the words "savage" and "primitive" come to mind, then use selvaggio. When you think of spontaneous and wild plants, you'll want selvatico.