The Lion Air plane was a Boeing 737MAX. The Ethiopian Airlines plane was a Boeing 737-800MAX.
The Lion Air plane crashed into the Java Sea about 12 minutes after taking off from Jakarta.
News reports Sunday said the Ethiopian Airlines plane "lost contact" six minutes after taking off from Bole International Airport. The plane had been en route to Nairobi, Kenya from the Ethiopian capital Addis Ababa.
The airline said in a statement that 149 passengers and eight crew members were believed to be on board but that they were "currently confirming the details of the passenger manifest".
The Ethiopian Airlines plane had taken off at 8.38 am local time. It crashed near the town of Bishoftu, some 60 kilometres southeast of Addis Ababa.
The Lion Air crash is thought to have been caused by an error in one of the plane's sensors, which forced the plane to repeatedly tilt its nose downwards.