BIG DIFFERENCE!
Corporations issue new shares to bring in capital for PRODUCTIVE purposes. They buy more infrastructure and hire more workers. Also issuing new shares is not really a debt since the money received has no obligation to pay it back.
National debt must be paid back with interest. And majority of money spent is non-profuctive. Currently federal Treasury is paying out in excess of 2/3 Trillion dollars for fiscal year ending on Sept 30, 2023.
Interest is paid back. No principle whatsoever, though.
Any principle "paid back" would be with more debt.