Are there any difference in the two?
Why?
Yes, there are differences. In one you’re sitting, in one you’re hanging. In one you’re pulling up, in one you’re pulling down. In one you’re balancing your body, in one your braced against support.
Pull downs are really easy to do the wrong way (pulling with your hip flexors and abdominals thus increasing the kyphotic posture so many people have nowadays). In pull ups this is practically eliminated. So I would stick to pull ups.
Pull ups are vastly superior to pull downs.