Architecture timeline:
Production timeline (end dates mostly correct):
As far as architecture goes, there's a couple main branches:
- TI-81 derivatives, with CPU inside the ASIC and three memory-mapped display drivers on a larger LCD support board
- TI-82 derivatives, with CPU (initially) outside the ASIC and a single port-mapped display driver
- TI-92 derivatives, based off of the 68k and running TI's AMS OS
- nspire derivatives, ARM-based and running the nspire OS
- TI-84 Plus CE, eZ80-based
- TI-80, running some weird 16-bit CPU
The original TI-81, from introduction in May 1990 to around the second week of April 1993, used the memory-mapped display architecture, then switched to a TI-82 motherboard with a smaller ROM IC and missing link hardware to reduce production cost. The TI-81 1.x firmware was ported to use the new TI-82 hardware and assigned firmware versions V2.0x, as the cost reduction eliminated the old design of the TI-81; it's basically a brand-new calculator with the same name, interface, and miserable screen readability. Nearly every Z80 calculator after the TI-82 used the TI-82's architecture, with notable exception of the TI-85-derived TI-86.
1996 through 2001 were pretty busy for TI. The TI-83 came out in 1996 as an enhanced TI-82, and shortly after in 1997 the TI-86 came out as an enhanced TI-85. TI introduced a Flash-based design of the TI-83 as the TI-73, running its own stripped-down OS; and introduced the TI-89 using a different architecture in the TI-73 housing style. People liked the TI-73 design so much that TI updated the TI-82 and TI-83 to use that new housing in 1999. At that same time, the TI-83 Plus was released; it did not replace the TI-83. The TI-82 and TI-83 were cost-reduced in 2001 to a cheaper-looking design ("Parcus") and only differed in firmware and housing color. Unfortunately, the TI-83 lost its high-contrast FSTN display in the Parcus update, now using the TI-82 Parcus' STN display.
The TI-73 was the first to add and use Flash memory, and introduced
a new housing design that eliminated the scratch-prone screen cover and added larger buttons. Design trials were successful enough that TI updated the TI-82 and TI-83 to use that design, and introduced the TI-89 and TI-83 Plus with that housing design. The RF shields on earlier models of those have
a TI-73 label on them. The TI-83 Plus is derived from the TI-73, not the other way around. The cosmetic design of the TI-89 is also derived from the TI-73 and was introduced around the same time, but as discussed later, is completely different internally.
The TI-92 slapped a 68000 on a handheld computer-sized calculator when 68000s were still being put in computers, so at the time it was pretty beefy -- and also a completely different architecture from what was being put into the 'regular' graphing calculators. The rest of the 68000-based calculators used this architecture, and the TI-89 is merely a size reduction of the TI-92 with
Plus module.
The TI-80 is an oddball and is barely a graphing calculator. The 16-bit processor and part of the ROM are integrated into an ASIC, and not a whole lot is known about the processor.
The TI-84 Plus C Silver Edition still uses the TI-84 Plus Silver Edition architecture, with a new screen attached with new supporting hardware. TI quickly figured out that a 15 MHz Z80 doesn't like to drive a port-mapped high resolution LCD; that model didn't last long. The TI-84 Plus CE that replaced it in 2015 is an entirely new design around a different CPU, a 48 MHz eZ80 with a much larger address space for memory-mapped IO. Additionally, the components used are easier to source than the 1990s-era Z80 core and low-resolution monochrome display.
Credits to Adriweb for some fact-checking 
. I think it would be nice to have a quick and dirty resource by year and architecture. 
