From the CAA: https://www.caa.co.uk/News/Boeing-737-MAX-Aircraft/
https://www.planespotters.net/production-list/Boeing/737/737...
The 737-700, -800 and -900ER, the most widespread versions of the previous 737NG,[10] are replaced by the 737 MAX 7, MAX 8 and MAX 9, respectively[61] (FAA type certificate: 737-7, -8, and -9[8]). The 737 MAX 8 entered service in May 2017,[2] and the MAX 9 entered service in March 2018.[62] The MAX 7 is expected to enter service in January 2019, followed by the MAX 200 later in 2019, and the MAX 10 in 2020.
The only difference, again AFAIK, is the passenger and cargo capacity, length, and the range.
The avionics are the same but because the planes have substantially different air-frames, the software parameters and possibly some functionality will differ. It's not unreasonable for differences in these flight parameters to be a factor.
Basically, the larger/more powerful/further forward engines on the MAX would cause the airplane to behave differently to other 737 variants in some situations, and MCAS is designed augment pilot input and allow the pilots to fly the planes as they would have flown other 737s (and allows pilots to fly MAXes under the same type ratings as previous 737 models). However, in edge cases (in the case of Lion Air, erroneous sensor input) the airplane might do something totally different from other 737 variants. Evidently Boeing didn't even require pilots to be told about MCAS, because all it (supposedly) does is make a MAX feel like an older 737.