While the 7M-GE [non-turbo] and 7M-GTE [turbo] 3.0 liter engines came in the Supra from years '86.5-'92 in the USA, Japan also had the 2.5 liter twin turbo engine in their '89-'92 models. Do not confuse this engine with the 1G-GTE, which was a twin turbo 2.0 liter.
The 1JZ has a bigger bore and shorter stroke than the 7M-GTE, which allows it to rev quite a bit higher. The engine is known to be more solid, stock for stock vs the 7M. Stock, the 1JZ also makes 50 more horsepower and about the same amount of torque as the 7M.
The 2JZ-GTE is the engine that came in the later model Supras [you know - the Supra that everyone wants] and the Japanese Toyota Aristo [Same car as the Lexus GS300, which unfortunately only came as non-turbo in the USA]. The 1JZ and 2JZ are very similar in construction. The 2JZ is "basically" a 1JZ with a longer stroke [making 3.0 liters of displacement with the same bore], larger injectors and different turbocharger operation [1JZ had smaller turbos which ran in parallel, while the 2JZs were a little bigger and run a sequential operation]. Because of this, 1JZ swappers in the US and Japan will sometimes buy a 2JZ short block under their 1JZ head when their 1JZ block wears out. This is known as the 1.5JZ.
Many people in the USA have swapped the 1JZ engine into their car, not only for the extra power and reliability, but also for something different, a challenge, and because the intercooler pipe routing for the 7M is absolutely ridiculous.
The manual transmission of the 1JZ is the same as the 7M-GTE - the R154 5-speed. The difference between the two engines using that transmission is the flywheels and bellhousings. The automatic transmission that came with the 1JZ was a bit different, however - the A342. This was different than the US A340.