To me there's a difference between these 2 topics, let me explain:
Browser support is browsers you're willing to support.
While browser testing is the act of testing and maintaining support.
Browser testing need not involve testing the full browser support list. In fact I find a graded view browser support makes this a bit clearer.
Testing every combination would take far too long and the client likely wont be paying for that extra time.
But why is this important?
When a client calls you up and says:
"There's a bug on OSX Firefox 23, why wasn't this picked up during browser testing?!"
You'll need to let them know the difference to explain clearly to the client why this was likely untested but assumed working (which is perfectly acceptable).
Eloquently put back to the client:
"It is not practical to test every combination of Browser, version and OS as there are so many. Instead we follow standard industry practice of testing the latest range of browsers, plus typically those which make up the majority of your traffic and sales. "
Depending on the browser support level, It's an a A or B grade browser, this would generally followed by:
"We'll take a look into this right away for you."
However in the case of a C grade browser, you would need to work out if this is a style tweak or core functionality.
"Unfortunately this is an older browser where fixing it can lead to complications. The cost of working on these older browsers is often not worth the return. If you'd still like us to work on it we can but we will need to quote for the time involved."
You could also then offer a service to the client of checking and testing the current highest converting traffic browsers. This could even be an ongoing / regular process you could offer.
Inspired by Yahoo, we use A, B and C grades for our browser support, here's an example of this:
"A" grade support
These browsers should be actively tested on, along side browsers that bring in higher amounts of traffic and sales on the site:
- Google Chrome Desktop ~ latest
- Google Chrome Mobile (Android) ~ latest
- Firefox Desktop ~ latest
- EDGE Desktop ~ latest
- IE 11 Desktop
- IE Mobile 11 (Windows Phone)
- Safari Desktop (Mac OSX) ~ Latest
- Safari Mobile (IOS / iPhone / iPad) ~ Latest
"B" grade support
Though not actively tested on, these browsers should work fine, and bugs can be fixed when reported:
- Google Chrome ~ previous recent versions
- Firefox ~ previous recent versions
- IE 10
- Opera ~ any modern version
- Android browser version 4+
- Mobile versions of the above browsers in recent versions, such as on IOS, Android and Windows Phone
"C" grade support
Core functional support only. These browsers may not offer all the same effects and may visually look different, however any issues that cause functional issues will be fixed, such as an issue that hides or makes it impossible to click a call to action button.
- IE 8 & 9
- Older browser versions than mentioned.