Two temples in Aurangabad. Ajanta Caves has 29 tickets and tours to book; Kailasa Temple (Ellora Cave 16) has no online ticket listed. The table and the two notes below put them side by side; the full pages have what to see, the ticket and the timing for each.
The Ajanta Caves lie in a remote gorge about 100 km north of Aurangabad, now officially Chhatrapati Sambhajinagar, so the real question is transport rather than tickets. Entry is bought at the counter at the visitor centre or online through the Archaeological Survey of India, with a lower fee for Indian citizens and visitors from neighbouring countries; there is no reason to pay a premium for a skip-the-line ticket, as queues are rarely long.
Most visitors book a private car with driver from Aurangabad for the full day, which is around three hours each way. Guided versions add a qualified guide at the caves, who makes a real difference in reading the murals, while cheaper options give you the car alone.
The Kailasa Temple is Cave 16 of the Ellora Caves, and it is entered on the general Ellora ticket bought at the counter by the main gate; there is no separate ticket for this temple and no reason to book online. Foreign visitors pay a higher rate than Indian citizens, a small extra charge applies to video cameras, and the ticket also covers the Buddhist and Jain caves along the same cliff.
How you get there matters more than the ticket. The caves are about 30 km north-west of Aurangabad, now officially Chhatrapati Sambhaji Nagar, and most visitors either hire a car with driver for the day or join a guided day trip from the city.