Let's make some sense of fitto and fitta. Sometimes they mean the same thing, as when they are adjectives, but they each have a noun form as well, which has little to do with the adjective meaning.
Fitto is an adjective meaning "dense."
Come la chiesa di San Matteo, nascosta nel fitto tessuto medievale della città, che appare così all'improvviso.
Such as the church of Saint Matthew, hidden in the dense medieval fabric of the city, which appears so suddenly.
Captions 8-10, Meraviglie S2 EP3 - Part 2Play Caption
In the following example fitto describes Iimpalcatura (the scaffolding), a feminine noun, so it has a feminine ending in this case: fitta.
Lavorando senza aiuto alcuno, nascondendo il suo David dietro una fitta impalcatura di legno per impedire a chiunque di vedere l'opera prima della conclusione. Fino al giungere al capolavoro: il suo David.
Working without any help, hiding his David behind a dense wooden scaffold to prevent anyone from seeing the work before its conclusion, before it became the masterpiece: his David.
Captions 33-37, Meraviglie EP. 3 - Part 13Play Caption
Il fitto is a noun that means the same as l'affitto (the rent).
Ho soltanto preso una casa in affitto, Ada.
I only rented a house, Ada.Play Caption
When you rent a place, you "take it as a rental," prendere in affitto. But when we talk about "the rent," as in "paying the rent," it's l'affitto. Pago l'affitto (I pay the rent). However, some people say, Pago il fitto. It means the same thing but is rather old-fashioned. You will find this definition of fitto way at the bottom of the page.
Keep in mind that there's the verb affittare (to rent) as well.
Una fitta is a stabbing pain.
In the following example, instead of fitta, Renzo says fittina to minimize it.
Ah, colonna vertebrale, già m'ha fatto una fittina.
Ah, spinal column, that's already given me a slight stabbing pain.Play Caption