Difference between Wyeast and White Labs?

So I recently bought ingredients for an APA at my LHBS (shout out to J&M Brewing in Novato, CA). I do 11 gallon batches so that I can ferment with 2 different yeasts to compare flavors in the finished product. For this particular brew I was going to buy Wyeast 1056 American Ale and White Labs WLP001 California ale. As I was being charged for everything the salesman asked why I was using 1056 and WLP001 as they are essentially the same thing (Sierra Nevada according to him). He suggested swapping out WLP001 for WLP051 California V Ale Yeast (Liberty Ale from Anchor according to him). I figured, why the h*** not and did so. As I was driving home I started to wonder if this was actually true. Are WLP001 and 1056 the same yeast (maybe slightly different but not noticeable)? What about Wyeasts and White Labs version of London Yeast? Irish Yeast? I think you get my point. If this is true I would consider doing Wyeast only as my White Labs vials tend to explode whenever I open them, no matter how carefully.

Thoughts or comments? Anybody ever try 1056 and WLP001 in a side by side taste test under controlled fermentation?

1056, 001, S-05 are all essentially the same strain, as Chico, as the house strain of Sierra Nevada

There are other similarities in other strains between the two producers.

Otherwise each produces similar but different strains and yeast are huge components of what your beer becomes

It really comes down to dry, smack pack or vial

Many of the yeasts between the two overlap and are essentially the same. Check online for yeast comparison charts. They will tell you which ones overlap.