Halal is an Arabic word for ‘permissible.’ So, wearing your watch, your shoes, etc., are considered halal (in general) . As well as eating chicken and beef. Halal can range from obligatory to undesirable, and covers virtually every subject. As it pertains to food, the term halal is a very broad term. It includes the way the animal was raised, its age at the time of sacrifice, the non-mixing with non-halal meats, the manner in which it was sacrificed, etc.

Dhabeehah (most transliterations spell it as: zabihah) is an Arabic word denoting the proper sacrificing of a domesticated animal, and specifically, animals sacrificed by a Muslim slaughterman with all the main necessary components: 

a. Muslim slaughterer (w/ sharp cutting tool)

b. healthy and age appropriate animal

c. saying a short prayer (e.g., Bismillah Allahu Akbar)

d. swiftly, but accurately cutting the animals throat   

If all the above is fulfilled, plus a little more, the meat will be considered halal for consumption. 

Both terms are sometimes used synonomously, but they signify two different aspects of meat that can be consumed. 

All of our meats are zabihah-halal 

(hand- sacrificed by a Muslim).