Confusingly, Italians would call Piedmontese or Lombard a “dialetto” as much as they would call Turinese a “dialetto”. The word basically means a dialect or regional language, depending on the context. There is also a political element to it—the Italian government has suppressed the regional languages for years, and even now does not recognise them as languages, against academic opinion.
To be clear, Italians would also (generally) refer to Welsh as a “dialetto” of English, despite the fundamental difference of Welsh and English. (In fact they would usually also often refer to the U.K. as “inghilterra”.) The word “dialetto” as currently used in normal Italian speech simply does not correspond 100% with the English word “dialect”, much like the word “camello” doesn’t correspond to “camel”.
The regional languages generally are not mutually intelligible, although this depends on which dialects two speakers speak, and how “stretto” (strong) the dialect is (I don’t know what the academic term for this is). So for example Vercellese (from Vercelli) is linguistically close to Novarese (from Novara) even though Vercellese is classed as Piedmontese and Novarese is classed as Lombard (despite being a Piedmontese city). The distinction is ultimately arbitrary—there is a gradation of dialects from Piedmontese to Lombard. Vercellese for example has many grammatical elements of Lombard (e.g. it uses the Lombard lü (meaning “he” or “him”) instead of the Piedmontese chiela).
Also, an older or more rustic speaker is more likely to speak a “stretto” dialect, because they’ll use more words and expressions originally belonging to that dialect (or to the regional language). Over the years, the regional languages have absorbed many words from Italian, replacing the traditional words. Now, the same thing is happening to Italian with English words (e.g. the word “goal” replacing “rete”, or “babysitter” replacing “tata”, or “shopping” replacing “spesa”—the English word in each case sounds more modern or cool to Italian speakers).
The linguistic situation is basically the same as with Catalan and Spanish. Catalan is as much a “dialect” of Spanish as Piedmontese would be a “dialect” of Italian. In fact, you could just as rightfully say that Italian is a “dialect” of Piedmontese. The difference is political, not academic.