Q:

Does "case" equal "declension"? 6 declensions for 16 cases?

I am somehow bemused by the sixteen cases of the Russian. On the other hand, I thought that there were only six kinds of declension. Perhaps these two facts are not contradictory, but the problem is that I am not aware of the difference between case and declension. During my only Russian course, I was given some declension tables with 6+6 endings: six endings for nominative, genitive, dative, acusative, instrumental and prepositional, plus six from their plurals.  
Can some (hopefully all) of the 16 cases in the aforementioned question be grouped, as to obey one of the six common declensions? If so, which cases obey which declension rules? If not, I'm afraid that one has to learn a 16+16 table.

A:

Case is a certain form of the word which is required by its grammatical role in a certain sentence.
For instance if you wanted to say "I gave money to …" (я дал денег …) you would have to put the subject into dative, because it is required by the grammatical construction of the sentence.
There are six traditionally recognized cases in Russian (nominative, genitive, dative, accusative, instrumental, prepositional) but some linguists describe up to 16 (as in the link you gave in your question). Not all words in Russian can form all of those, though.
Declension (in narrow meaning) is a certain paradigm which defines how exactly a word is put into a certain case.
There are three commonly recognized declensions in Russian, plus several special cases (indeclinable nouns; ten words enging in -мя; words мать, дочь; words небо, чудо; pronominal paradigms in words like швартов, кабельтов, ничья etc.)
So actually declensions and cases are rows and columns in a table which stores endings in its cells.
When you want to say "I gave money to dad" in Russian, you look up the word "dad" in the dictionary and find it to be папа (1st declension). As we said above this phrase requires the subject to be in dative.
Then you look up what's the sg. dative ending for 1st declension, find it to be -e and say: я дал денег папе.

