"Your neighbor Omar is a good translator, Sam."
Translation:جارَك عُمَر مُتَرْجِم جَيِّد يا سام.
Well, as a beginning, the sentence here is not accurate, because it should be جارُك (járuka) - your neighbor.
Now, to explain the differences, we have to forget about the possessive suffix at the end (-ka) ـك.
In Arabic, the last letter in the word (or generally speaking, the ending) changes according to the position of the word in the sentence. In other words, changing the ending of the word is a grammatical feature. There are mainly 3 statuses or changes that might occur to a word according to its position or according to what influences the word:
Nominative: This is the normal case of the word, and it gets the ending of (-u) as in جارُ (járu). Nominative is a collective status actually, and in Arabic grammar there different classes, like subject, predicative and many others no need to mention them here, but the base line is: Nominative is when nothing affecting the word or noun. This is the normal status of the noun, and it gets (-u) ending.
Accusative: When the noun is affected by the action of a verb (as well as other situations), the noun gets (-a) ending, as in جارَ (jára). However, such ending is actually common in other statuses like for adverbs, but English books use the term Accusative collectively for every status or situation where a noun in Arabic ends with (-a). In Arabic grammar books, naming system is totally different.
Genitive: This name for this category is quite off but I will go with it just to explain. In this status, the noun usually gets a (-i) ending, such as in جارِ (jári). This ending occurs when the noun is bound to another noun by a genitive relation (hence English books associate it with the Genitive), and it also occurs when the noun is affected by some preposition articles like إلى (ilá: to) or مِن (min: from)... etc.
I hope the explanation is easy to digest here. The naming of these categories is quite different between Western books and Arabic grammar books - so I went along Western system here just because they use terms that best fit Indo-European languages the most so it might get closer to understanding. Hope that helps.
Away from the audio here, because it is bad and wrong at some aspects; What you are saying is true in fact but in dialects of Egypt and the Levant. In standard Arabic (fusHa), the ending for masculine (your) is -ka (sometimes the "a" is omitted at the end of the sentence), while for feminine (your) it is -ki (and the "i" is kept usually to clarify it is a feminine).
In the dialects, the tendency seems to be to reverse the order of -ka and -ki and make it as -ak and -ik.