What is the difference between selling the shares and selling the assets to end a business?

When selling the shares, the corporation still exists and is bound by its contracts while when selling the assets, the purchaser is only bound by liens on those assets.

When selling shares, the corporation ceases to exist and the purchaser is only bound by liens on the assets while when selling the assets, the purchaser is bound by the corporations contracts.

Selling the shares changes the ownership of the corporation while selling the assets does nothing to its business.

Selling the shares results in the corporation having no business while selling the assets results in new ownership of the corporation.

There is no difference. Both result in corporate dissolution.