Name for type of adjective such as "porcine"

Basically the description given is the description used. Since English has so many words that come from Latin (either straight or aged in Norman French), it has tended to borrow whole sets of words formed on individual roots.

Thus, denominal "adjectives" in -al/ar were already formed in Classical Latin. Of course, classical grammarians would simply have called them Nouns -- "Adjective" is a modern Part of Speech.

There is no special term for these words, which all have their own peculiarities. Don't forget, every word in the language has its own individual history, the result of its millions of daily uses, in the mouths of millions of speakers, over thousands of years.

History is not something that happens to classes of words as a group, but to each word in its own way. Classification and generalization comes later; nobody noticed the Great Vowel Shift while it was going on, after all.

Some terms for the groups named by such words (unfortunately not quite what you asked about) are nominal category and nominal group: “a group of objects or ideas that can be collectively grouped on the basis of shared, arbitrary characteristic”.

The word pertainym may apply; of which, wiktionary says: “(computational linguistics) a word, usually an adjective, which can be defined as "of or pertaining to" another word”. If I understand correctly, floral, porcine, and piscine are pertainyms.

In all the cases presented the English word really means "having the qualities of" the target, while the classical word means "pertaining to". For example, fishy means "having the qualities of a fish" while piscine means "pertaining to fish". And for a non-biological example: fraternal means "pertaining to brothers" while brotherly signifies "having the qualities of a brother".

jwpat7 pointed out the term "pertainym" which is probably the closest. But I believe now that the reason there is no widely recognized English term for the "pertaining to" form is that English simply uses a noun adjunct for that very purpose.

Using the three example words from the question plus a couple of others you could use the classical forms presented, or for the English form you just use the noun itself:

Classical            English
Floral container     Flower box
Porcine enclosure    Pig sty
Piscine reservoir    Fish pond
Nephrotic syndrome   Kidney disease