Old English had a true genitive case, but it has been displaced by the possessive. In Old English, "Sally's book" would have been written "Sallyes book" and "Sallyes" would have been the genitive form of "Sally". You also could have said "book Sallyes" but you cannot today say "book Sally's". Later the apostrophe was added to replace the "e", so it might seem like nothing really changed. That would be false. Formerly, nouns were used more often in genitive form than the possessive is today. Also, the genitive could be moved about in the sentence. Now, however, the possessive always goes in front of whatever it modifies. It is more limited now. For example, formerly it would have been natural to say "dayes beginning" for the beginning of the day. Today, it is not wrong to say "day's beginning" but people wouldn't say it as often. More important, the word order used to be flexible. You could have said "beginning dayes" and the meaning would have been perfectly clear, whereas today "beginning day's" sounds nonsensical. It is sad that English lost its genitive case because that loss diminished the expressive power of the language.

In grammar, the terms "genitive" and "possessive" are closely related, and they often refer to the same grammatical concept, but there are subtle differences in their usage and interpretation. Genitive Case: The genitive case is a grammatical case used to indicate relationships between nouns. It typically expresses possession or association. In English, the genitive case is often marked by the use of an apostrophe and an "s" ('s) to show possession. For example: "John's car" or "the cat's tail." In some languages, the genitive case is expressed through inflections or changes in the noun form itself. Possessive: The possessive form, on the other hand, is a broader concept that includes not only the genitive case but also other ways of expressing possession or ownership. In English, the possessive form is commonly used to indicate ownership or belonging and is marked by an apostrophe and an "s" ('s), similar to the genitive case. The possessive form can also be expressed using the preposition "of." For example: "the car of John" or "the tail of the cat." In summary, while the genitive case specifically refers to a grammatical case used to show relationships between nouns, the possessive form is a more general concept that encompasses various ways of indicating possession, including the use of the genitive case. In English, the terms are often used interchangeably when discussing possession and relationships between nouns.

'Possessive' can be considered as a sub-class of the 'genetive.' Modern English doesn't have a true genetive case, so it's just the 'possessive case' in English. Latin, slavic languages as well as many other languages have more extensive case systems.