The majority of scholars hold the opinion that Zakat is to be both paid and received by Muslims. Other forms of charity such as Sadaqah can be given to Muslims and/or non-Muslims alike.
Zakat cannot be given to:
The rich (except when such are among the workers of Zakat).
The strong and able poor e.g. those capable but not willing to work
The heretic, apostate, those disbelievers actively fighting Islam
The family of the Prophet (peace be upon him) – The names of the Prophet’s tribes are Banū Hāshim and Banū Muṭṭalib.
(While this is generally true, as per our Zakat Policy, in line with the opinion of some scholars, we at NZF support people from the Prophet’s family with Zakat)
Note, the Hanafi school does not permit a wife to give Zakat to her husband. However the Shafi’i school permit the wife to give her Zakat to her needy husband.
