I assume pretty much all toyota spare rims are going to be the same on offset and lug pattern.
Nope.
The spare from your truck has about 3/4" less backspacing than one from a 2003+ 4Runner or 2005+ Tacoma. Toyota differentiates the 16" steel spare wheels by changing the hole by the valve stem. On the 2005 and newer Tacoma it's an oval hole while on the early trucks all the holes are round.
If you're getting a 17" wheel from a newer FJC, 4Runner or Tacoma they're all round, too. That's because there was no option for 17" wheels on the earlier trucks. I think the backspacing is increased on those, too.
Now I'm pretty sure the newer wheels will fit over the caliper (pretty sure) on older truck still but your track might be changed and it's probably not ideal if you mix-and-match. Going the other way is no problem. I run 3rd gen 4Runner wheels on my 2008 Tacoma. Partially for the look but also to give me more room between the tire and control arm.
42601-AF010 (1995-2004 Tacoma) and 3rd gen 4Runner.
42601-AD030 on 2005-current Tacoma. Notice the oval hole.