Buying a business can be structured as a purchase of its assets or of its equity, and the difference is mostly about what the buyer inherits.
Stock purchase. The buyer acquires the entity, and with it everything the entity owns and owes — including liabilities nobody identified. Simpler where contracts, licences and permits would be difficult to transfer, because the contracting party does not change.
Asset purchase. The buyer acquires identified assets and assumes only the liabilities it agrees to. Cleaner from a liability standpoint, and more work: each material contract may need consent to assign, and licences and permits often must be reissued.
Where the clean line blurs. Successor liability doctrines can attach certain obligations to an asset buyer despite the structure — commonly where the transaction is a de facto merger, where the buyer is a mere continuation of the seller, where the transfer was to escape liabilities, and in some jurisdictions for product liability or certain employment and environmental obligations.
Other drivers. Tax treatment usually differs materially and often decides the structure. Consents required under change-of-control clauses can make a stock deal harder rather than easier. And employment relationships transfer automatically in a stock deal but generally require rehiring in an asset deal, which has consequences for benefit plans and for notice obligations on larger transactions.