Does anyone know if there are enough similarities between the two to be able to use many of the TI-84+ CE examples and routines on the TI-89?

No, you use the examples provided by the TI-89 toolchain.

So even though they can both be programmed in C, they are very different? I haven't taken a close look at C for the CE yet.

C is a language. How you interact with things such as the screen is different.

Ok, got it. Thanks!

Right. Nearly all functions provided by, and nearly all file formats used by, the respective OS of the TI-eZ80 series and the TI-68k series are very different. That's caused by the different processor architecture, the different pieces of hardware (screen dimensions and depth, keyboard, USB controller, etc.). Trying to make an abstraction layer between the TI-68k series and the TI-eZ80 series would yield fairly inefficient code, and we can't really afford that on such underpowered machines as these graphing calculators are.
There is a slight level of similarity due to functions mandated by the C89 and/or C99 standards, as well as the fact that for the community programming framework, Mateo reused some concepts implemented by so-called "kernels" on the TI-68k series - with good reason. But that's not much.

Only higher-powered graphing calculators (all of which remain far weaker than pretty much any smartphone, even several years old) have enough power to withstand abstraction layers. One such layer is the Linux kernel, there are unofficial ports of Linux for the Nspire series and for the HP Prime G1. However, nothing (yet) for the recent, much more powerful HP Prime G2 which does not accept custom firmware as easily as the HP Prime G1 does.