There are many differences in terms of rules governing the two series. Be it engine displacement, number of cylinders etc. One big difference is F1 cars use high octane gas (petrol) and Indy cars run on ethanol (alcohol). You see in many Indy car accidents where the car catches fire all you see if the waves from the heat but no flames since ethanol burns “clear”.
Formula 1 has massive development budgets with huge facilities with wind tunnels and high tech fabrication departments and hundreds of engineers. So the amount of money spent on F1 dwarfs IndyCar team budgets.
Some other differences:
Indy cars race predominately on oval tracks with a few street circuits. F1 never races on oval tracks.
F1 cars have better brakes and stop much faster than Indy cars
F1 cars have much more aerodynamic grip (downforce) than Indy cars
Indy cars have faster straight line speed due to their oval track usage
F1 is much more popular worldwide than Indy cars
F1 races in many different countries across the globe while Indy car races mainly in US