In corporate transactions and litigations there are two types of sale of a business: a stock sale and an asset sale. They are very different and both are very viable.
A stock is a piece of ownership in a corporation. In limited liability companies, the ownership interests are referred to as units or interests. When a buyer acquires your ownership interest, whether stocks or membership units, they are just stepping into your shoes. The company name continues, the contracts in place are unchanged, and so on. The biggest change will be in replacing you as a personal guarantor with the buyer.
An asset sale is where your company (not you) sell the inventory, contracts, real estate, and other tangible assets to a buyer. What is usually excluded is the company name. Your ownership in your existing company is not part of this transaction. The buyer take title to the assets and you wind down the company you still own, but which does not really have any existing business.
Why is one sometimes preferred over the other? The primary issue is taxes. Buyers and sellers will rely on their accountants for the most tax preferential acquisition. Either way taxes will be paid and a buyer and a seller have a different interest in whether it is an asset sale or an ownership sale, but that's where negotiating becomes so critical.
Corporate transactions are very, very active right now. If you are in the fray, let's get together and guide you to closing!