There seems to be no difference between the two. specific goods are identified at the time of sale. i guess between persons, companies, etc. This is opposed to unascertained goods, where the products or services to be transferred are not identified at the time of the agreement. Ascertain=to make certain of.

The sources I found seem to say that ascertainable goods are specific goods. The comparison is to unascertainable goods. The terms are used in a contract of sale to specify whether or not the exact property being purchased has been selected already.

Your Picasso example does not work outstandingly well: a Picasso would be that painting and no other, so it would always be (a) specific good; (an) ascertainable good. (It is a specific painting; one can always ascertain which painting has been/is being sold - though that is a non-legal usage of those words.)

The egg example seems more apt.

A contract for sale, for 100 dozen eggs is being written. The question is, may the seller pick any 100 dozen eggs from the seller's store of 1,000 dozen eggs (unascertainable goods), or have the eggs which compose the 100 dozen being sold already been selected and set on a pallet and wrapped for sale (specific, or ascertainable goods: you know exactly which eggs they are.)

I cannot say how this would affect any damage claims. It may have implications in a 'when does responsibility transfer' sense, but I am not a lawyer and do not know whether anything legal inheres automatically. And, remember, the law may differ from one country to another.

Chest-of-Books Handbook of the Law of Sale of Goods: Ascertained or Specific Goods, UK

Wikipedia: Sale of Goods Act 1979: Part II, contract formation UK. This link is part of the way down the article. Start where it says "Under Sections 6 and 7, . . . ." This speaks to warranty of suitability issues, but again, to figure out what a court would probably decide about damages, you need a lawyer.

Scroll down and see also Part III, effects of the contract, especially Rule 5; and Part V, rights of an unpaid seller, where it is titled "Consumer requires replacement or repair". Remember this is all UK.

Glossary of manufacturing terms: Specific good This site is a little clunky. I've linked to the top of the "sp" section; the entry is about five down from the top.
Same site: Ascertained goods
Same site: unascertained goods These entries suggest to me there may be a small difference between specific goods and ascertained goods, but heck if I'm sure about that.

Specific goods are those goods which one you can categories and in ascertained you can say nearly related things of you demand.