Are there two types of planting/hardiness zones?  According to here, I am 9B.  But according to here, I am 8B.  Is one of these types more commonly used?

Most people us the USDA zoning only.  

It looks like the second page is using the outdated USDA zones "The 1990 USDA Hardiness Zone Map"

The USDA zone map has been updated in the last couple of years to reflect changes, so you are probably 9b.

I am a 9B, then.  :)

Sure as we prepare for whatever the zone maps tell us, nature sends us a couple of zones lower and everything dies.       

The climate zone designations have value to help understand the length of your grow season, average temperatures, heat units available from this you can determine whether the season in your zone is long enough and hot enough to ripen the varieties you want and how much winter protection you will need.

The problem is that the actual weather varies so much.  All it takes is one period of extra cold than what the plant can take and you will be starting over.

Last year proved that you are better to plan for the coldest possible winter so that your treasured fig harvest continues unabated. 
 
  

Im in zone 6. (A or B really doesn't make a difference.) With last winter's damage we take no consultation in what a zone map says. "It says right here I'm supposed to not have harsh winters." For me the difference between zone 8 and 9 is the difference between $10,000,000 and $11,000,000. I'll gladly take either one. Yes the trend has been that the zones are shifting to change my zone a little, every little bit helps.

There are also local micro-climates to consider. If your trees are on a hill facing the sun, or at the bottom of a valley floor where cold air pools.

The zone map is a useful guide to point us in the right direction, the rest is up to us.

Everyone should keep in mind zones represent average winter lows from 1976 to 2005. That means some winters will be colder, some will be warmer.

I'm in Zone 6b, which means average winter low of 0 to -5 F. Our low last winter was 0 F, so that's spot on. However, the weeks of single digit temperatures is what killed off so many plants, not solely the temperature.