From a tax perspective, there’s some big differences. This is not financial or tax advice, so talk to an accountant or tax professional about this if you need to get serious about it (too late for this company, but not the next)
The sale of your company was an asset sale, which means the amount you made from the sale will be taxed as income. That’s fine for the size of the deal and low complexity of the product. As you said, you sold some code, IP, and design.
If the transaction was much larger, say $1m+, you’d be pushed to the top federal and state income brackets and be paying a lot in taxes. Top federal income tax rate is 37%.
Most larger companies are C-corps, which is a boring way of saying they issue stock, have shareholders, and a board of directors. It’s a more complicated structure, but it’s absolutely necessary if you want to bring in outside investors and/or know you’re going to build a high-growth company.
Under this arrangement, the thing that’s sold is stock. Just like you buy and sell MSFT or AAPL. Selling a C-corp means you sell over 50% of the company stock to a buyer and they control the company. No IP, design, code, or assets are sold—what’s sold is control to all of those things.
Back to taxes: the seller pays a capital gain tax rate, which depending on more factors worth enumerating here, come out to a little above 15%. There’s also this thing called qualified small business stock, which discounts that 15% rate on the first $10m of gains if you’ve held that stock for more than 5 years and sold it (it’s more complicated then that).
The shorter answer to your question, “what more is in a company?” — equity!
That might be true in the US, but in other jurisdictions a sole-trader or partnership can also attract lower tax rates on the disposal of assets or the whole business including 'good will'. In the UK this could probably get entrepreneurs relief as well, taking it down to 10%. Speak to a tax accountant of course.
At least in Western law, a company a legal entity, but that is just me being pendantic. More importantly, a company to me is something which has employees and is at least somewhat able to sustain them, even only by burning money. So I would not even count self-employment as having a company, only in the strictly legal sense. To me, you literally need company to have a company.
Edit: Still congratulations to you and thank you for sharing!
This is a nonsense definition. You are describing an incorporated company as if it is the only kind. There are unincorporated companies, sole traders and partnerships turning over millions. No a company does not need employees.
You do not give any new input. Everything you said has already been said. Except of course for calling my explanation nonsense, which unfortunately is not only rude, but also false.
Natural language is not boolean algebra or legal text. Most people think of employees when they talk about a company. Hence the word company as in "having company". What most people think is what defines a word. That's how language works.
Of course you can call selling a software (everything OP listed as sold can be classified as software) selling a company. I do not want to demean what OP did. If he were to insist on having sold a company and not a software project, it would just sound a bit like the guy on LinkedIn calling himself CEO of his company, while being self-employed working out of his basement. (Not that OP does any of that, again OP did great!)