“Immigration” is about the people traveling from one country to another. It’s sometimes called “passport control” or “border control” depending on the airport. “Customs” is about the stuff those people are carrying with them.
In many airports, immigration is a mandatory process that involves speaking with an immigration officer who stamps your passport, while customs is an optional process; if you have nothing to declare, you don’t need to speak with an officer. You can go through immigration without your luggage, but customs will be located after baggage claim.