Just want to know why they look/operate differently in different states/territories when in other countries, including Canada, have nearly identical installations throughout their jurisdictions.

Different DOT standards maybe? In Australia the only difference is whether the target boards are solid black or have a white outline.

That’s what I’m thinking, but I’m not entirely sure. So in your country, the states have little to no authority in terms of traffic light designs?

We have only 2 main manufacturers of signals, there are other slight differences but as a general rule the country has similar standards.
Here is an intersection in Victoria.
https://www.google.com/maps/@-37.8395183,144.9956557,3a,15y,322.28h,90.33t/data=!3m7!1e1!3m5!1s_b_85QSGMzPRgWg22kGZTQ!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fpanoid%3D_b_85QSGMzPRgWg22kGZTQ%26cb_client%3Dsearch.revgeo_and_fetch.gps%26w%3D96%26h%3D64%26yaw%3D153.43423%26pitch%3D0%26thumbfov%3D100!7i16384!8i8192?coh=205409&entry=ttu&g_ep=EgoyMDI0MDgyMS4wIKXMDSoASAFQAw%3D%3D
here is an intersection in Canberra
https://www.google.com/maps/@-35.2359471,149.0580235,3a,15y,126.98h,92t/data=!3m7!1e1!3m5!1s2hofykmzrRewn8-yCvvaTQ!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fpanoid%3D2hofykmzrRewn8-yCvvaTQ%26cb_client%3Dsearch.revgeo_and_fetch.gps%26w%3D96%26h%3D64%26yaw%3D293.88797%26pitch%3D0%26thumbfov%3D100!7i16384!8i8192?coh=205409&entry=ttu&g_ep=EgoyMDI0MDgyMS4wIKXMDSoASAFQAw%3D%3D
As you can see, there is very little variation in the SIGNALS, the poles are essentially the same, just different colors.

In my area, the province dictates the traffic signal standard but the municipalities have a bit of leeway in determining what gets installed.

For example in my province I've seen the following installs:

Yellow signal with yellow backplate - The default signal.
Yellow signal with yellow backplate, grey on the back - used in some municipalities.
Black signal with yellow backpalte - used in some municipalities.
Black signal with black backplate - used in some historical districts.

Works fairly the same way here. But here, the states dictate how the signal is installed, such as my home state banning permanent span wire setups and most of them using black doors, visors and backplates but yellow housings and most don’t have reflectors on the backplates. Some states, like Michigan, use fully yellow signals on span wires, Florida uses span wire signals that span across the intersection and are green in color while Mississippi currently installs fully black signals, poles and masts.

Speaking of Canadian traffic signals, even Canada doesn't have uniform traffic signals throughout the country. Quebec (and some parts of Atlantic Canada I believe) is very much into horizontal traffic lights. Oftentimes, though not quite as much as it used to, red lights are also doubled, which is a nice safety feature that should've been adopted continent-wide, IMHO.

Texas often does the same thing for red arrows.