Allah says in the Quran what could be translated as:
“Made lawful to you this day are At-Tayyibat [all kinds of Halal (lawful) foods, which Allah has made lawful (meat of slaughtered eatable animals, etc., milk products, fats, vegetables, and fruits, etc.). The food (slaughtered cattle, eatable animals, etc.) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them…” (Quran 5:5)
Aisha (RA) reported, that some people said: O Messenger of Allah, some people bring meat to us, and we do not know whether they mentioned the name of Allah over it or not. The Messenger of Allah (ﷺ) said: “Mention the name of Allah over it and eat” (Bukhari).
The Prophet (peace and blessings of Allah be upon him) ate meat slaughtered by the Jews and did not ask questions.
The difference between Zabiha and Halal meat is the way it was slaughtered.
Zabiha is considered the most appropriate and correct way to slaughter animals for consumption as per the prescriptions in the Quran. Zabiha is the way that defines how the animals must be slaughtered in a humane way and it is a hand slaughter.
Halal is considered legitimate and lawful as per Islamic beliefs and is believed to be largely a humane method of animal slaughter and it involves machine handling to the animals being slaughtered.
As for the slaughtering of animals, the USA has laws in place, where the animal cannot be killed in too cruel of a fashion, which would mean that most meat establishments would cut the jugular vein allowing the blood to spill out. based on that, some scholars deemed it permissible to eat from the meat of the people of the book.
However, many other scholars have a lengthy rebuttal to the above-mentioned assessment and they don’t deem it permissible to eat from the meat available now in the lands of Christians/Jews.
Our opinion in the office of Imam of IAR is to try your best to eat meat slaughtered by Muslims especially nowadays it is available everywhere in Muslim grocery stores and local restaurant depots.
If you are on travel within the United States and can’t find zabiha meat, then you can eat meat with the fiqh understanding of the scholars who deemed it permissible.
Among a number of scholarly opinions, three could be summarized as:
1. Prohibition of all non-zabiha meats e.g. most grocery store foods (the reason why varies, e.g. that slaughtering methods differ or that providers do not fall under People of the Book, but the conclusion is shared).
2. Allowance of chicken but pious caution of beef/lamb.
3. Allowance of chicken, beef and meat of other animals is not prohibited for consumption in Islam.
For additional detail, you may review articles such as these:
and the fatwas of the AMJA council at www.amjaonline.org such as: