Throughout the series, the characters use chassis codes to refer to cars rather than actually saying the name of the car. This is a common Japanese auto industry term to easily refer to a car and its year without having to give a drawn out explanation. The S13 refers to the RPS13 SR20DET Nissan Silvia (Japan only) made from 1989-1994. The Silvia made between 1995 and 1998 was an S14, and 1999 to present is the S15. R32 refers to the BNR32 Nissan Skyline (Japan only) made from 1989-1994. FC refers to the FC3S Mazda RX-7 made from 1986-1992. FD refers to the FD3S Mazda RX-7 made from 1992-2002. EG6 refers to the EG6 Honda Civic 3-door hatchback made from 1992-1995. And most importantly, 86 (or 'Eight-Six') refers to the AE86 Toyota Sprinter Trueno, known in the U.S. as the Toyota Corolla GTS, made from 1983-1986 (the Trueno is also known as the hachi-roku, however 'hachi' and 'roku' are just the literal Japanese words for 'eight' and 'six').
Keiichi Tsuchiya, well known as the 'Drift King' of Japan and a pioneer in the field of drifting, was on-hand as an advisor to the show. He also makes a brief cameo in episode 24 during a phone call to Bunta Fujiwara
The Nissan 180SX, which Kenji drives, is a hatchback variation on the Nissan Silvia (both Japanese only cars). These cars are known in the U.S., however when the Silvia and the 180SX came to the states, they lost their turbocharged 2.0 liter SR20DET engine and became the Nissan 240SX, which was given a non-turbo 2.4 liter engine known as the KA24E. Despite the fact that the Silvia (a coupe) came with fixed projector headlights, the 240SX coupe was given pop-up lights like the 180SX due to U.S headlight regulation permitting cars with certain headlight height to be sold (for this reason, the American 240SX is also known as the Onevia, a combination of a 180SX front onto a Silvia, whereas Mako and Sayuki's Sil-Eighty is a combination of a Silvia front onto a 180SX).
The original comic had brand stickers on the racers' driver doors (Bomex, Greddy, HKS, etc). The animation studio could not obtain licenses for the brand names, and replaced them with generic stickers instead (Max Speed, Shift Down, etc).
Haruna Mountain was renamed "Akina" in the comic/series because creator Shuichi Shigeno originally intended all places in the series to be fictional/based of actual places. However, he does away with this practice on later courses, but the name "Akina" sticks for Haruna Mountain.
Early in the TV series, many of the cars are either missing the proper badging for their cars, or the badging has been significantly altered (the most notable are the "Trueno" on the front of Takumi's AE86, and Nakazato's missing "Skyline" on the rear bumper and altered GT-R badge). This is due to the animation studio not having licenses from the car manufacturers at the time. Later on in the series, the badging is fixed and all the cars have their proper badging. However, correct badging appears in flashback scenes of episodes that originally didn't have badging on their cars.
When the series first aired in America, the popularity of imported JDM cars skyrocketed. Vehicles like the Mazda RX-7 and the Nissan Silvia became extremely popular with tuners and drifters alike. Most JDM vehicles gained in price, and nowadays this is called "Drift Tax".
Impact Blue's SilEighty was originally just a simple body kit fix for the 180SX to have the fixed headlights of a Silvia S13. Nissan, noticing how popular the body fix was becoming among tuners, ran a limited edition "official" SilEighty. These are numbered and highly collectible.