There are two separate Israeli ministries here, not one combined ministry:
1. Ministry for Diaspora Affairs and Combating Antisemitism
This ministry focuses on Israel’s relationship with Jewish communities abroad and on policy and programs related to antisemitism.
The official gov.il page lists Amichai Chikli as the minister. 
2. Ministry of Aliyah and Integration
This ministry handles aliyah (Jewish immigration to Israel) and immigrant absorption services, including benefits, appointments, employment support, and services for returning residents.
The official gov.il pages show Ofir Sofer as minister. 
So if you meant “diaspora and aliyah” together, the key distinction is:
Diaspora Affairs = Jews living outside Israel, global Jewish relations, antisemitism policy
Aliyah and Integration = Jews moving to Israel and settling there 
If you want, I can also give you:
• a 1-minute overview
• the Hebrew names
• or a comparison with the Jewish Agency.
#Israel
#Ministry_of_Aliyah
#Diaspora