I have a lot of thoughts on this issue....
First question is, if you are in CA, why are you growing in pots to begin with? Why not just grow in ground? Will be a lot less labor and expense and you'll probably get more fruit.
The photo isn't that clear, but to me it looks like the stuff you got at Summer Winds Nursery has quite a bit of wood pieces mixed in. Usually you want it to be almost entirely bark, if possible. It's not feasible to separate it by hand.
Around here soil conditioner is sometimes bark, but sometimes it's just composted leaves, which is very different. Have to poke a little hole in the bag and investigate. I think they will use either to make the product, depending on what's available/cheaper.
To answer the question, "What's the difference between pine bark and pine fines". There may or may not be a difference, depending on how they are labeled. In my experience, if it's called pine bark mulch, it is usually a fresh product and hasn't been composted or aged at all. Now if it says aged pine bark, or pine fines, it should be partially composted/aged. The aged product is better because it retains more water. On the other hand, it is heavier (probably because it contains more water). In my opinion the aged product is better. However, for me it's harder to find. So if I am forced to use the fresh product (as is often the case), I will make sure to add the peat moss, maybe even a little extra, to make it more water retentive. After a year or two, the fresh product will naturally deteriorate into the aged product, and then eventually into mush.
If I can get the aged product, I don't even add peat moss. Just some fertilizer, lime, and slow release fertilizer (osmocote, for example).
I don't see any point in sifting. Why would I sift away the small particles, and then add in peat moss (small particles)? Just not worth the work, in my opinion.
Also, I think adding the perlite is totally unnecessary and just adds expense without improving the characteristics of the mix. It may have usefulness when rooting cuttings, but when you get to larger sized trees, it's not helpful.