Actually, we're getting confused here (not to mention hi-jacking the thread - sorry
).
There are actually 2 (arguably 3) cars 'named' the Dino. The 206/246GT (made by Ferrari) and the Fiat Dino (made by Fiat). The original 308GT4 was also badged a Dino, but only for a short time.
The Dino was actually the engine. An Alloy Block DOHC 65° V6. It was first produced with a displacement of 1987cc (considered 2.0L - '66-'69) and later with a displacement of 2418cc (2.4L - '67-'73).
Ferrari didn't have a platform in which to homologate the engine for formula 2 racing, nor did they have the production facility to produce one. So, parent company, Fiat designed a chassis and Pininfarina produced a Spyder body and Bertone produced the Coupe' body. This was known as the Fiat Dino and was produced from 1966-'73. It was never officially imported into the US, though a few hundred made it in. The Dino used in the Fiat was slightly detuned and marginally less powerful.
The Formula 2 regulations changed in the meantime, making the engine obsolete - Ferrari never competed with it in Formula 2.
Pininfarina in the meantime was urging
iL Commendatore to produce a mid-engined street car. Enzo had always thought they were too dangerous for the General Public and so had refrained for years from producing one.
He finally relented, but insisted they "
not use a Ferrari (V12) but a Dino (the V6)". This became the 206GT with the 2.0L Dino and later, the 246GT with the 2.4L Dino.
As mentioned, they also wanted to distance the Dino equipped cars from the Ferraris and so marketed it under the brand Dino. Enzo felt that only the V12 cars should be considered Ferraris.
But, when in the mid-70's, Ferrari realized they didn't have a branded car for sale in the US (their #1 market), they instructed their US dealers to rebadge the 308GT4 (originally the Dino 308GT4) as a Ferrari removing the Dino badge completely (you can see where the early cars had a concave rectangular indentation on the hood and rear hatch to accept the Dino badge). And also instructed them to fix the Prancing Horse above the Dino badge on the hood (keeping the Dino badge in place) for the '74 246GTs (the '74 is the only official Dino to have a Prancing Horse, except Pininfarina's personal 206GT). European dealers shortly followed suit, but on their own.
Many Ferrari badges were added later to earlier cars by their owners, but interestingly, in the past few years as Dino prices have skyrocketed, these owners are now pulling the Ferrari emblems to restore originality.