"Let me try a rhetorical question with you."

Yes, please. Because we have to be using Terminology to mean the same things.

"You own a registered business with tax ID. The business performs work for a client. The business bills the client for the month of February. 50 hours, $2000K. How do you record that?"

That's a Sale.

"You want all the $2000 to stay in the company account."

This is worded very oddly, and that's why I am trying to help. The use of the word "Account" is too generic. You make a sale of $2000. Are you expecting the customer to Pay or not?

Starting there:

The Sale is recorded as a sale. There is either the expectation of Payment or there will be a Discount given, reducing the amount to be paid to no less than $0.

"You may later decide to withdraw money from the business to pay a business expense from the $2000."

That's not a good way to think of anything related to Cash Flow. What you are now doing is mixing Banking with the reasons there might be funds in the bank. They don't link like you are thinking of it.

Each activity stands alone. Example:

You make 2 sales for $2,000 each. Both Customers only pay Half. You write off the other Half. Now you have $2,000 in the Bank. You do whatever applies with the money in the Bank. It isn't "from" sales. Sales is just Sales. If you make one $2,000 sale, and then adjust it to $0 by a write off or discount, you still have the Sale recorded. You have the Contra-income (contra means "opposite"). You have no new money in Bank.

When a customer pays you, that sale is now the income (and maybe sales tax liability). Whether that money went to the bank or went to landlord, doesn't change Income. It changes Bank; either it all went to bank or it did not.

"For sole proprietors, credit the Owner’s Draw account. It’s located in the Equity section. Create one if it’s not already there." <== Does Not Apply for You

Drop any consideration of Draws. You are not changing anything to do with Equity. Corporations don't give Draws to anyone.

"For partnerships, credit each partner’s investment account according to who paid what. If the investment accounts are not there, create them. They are Equity accounts."

Again, this is Not your issue. Nothing about what you are asking help with is an Equity issue.

"For corporations, I suggest you credit a Shareholder Loan account. If you don’t have a Shareholder Loan account, create one as an Other Current Liability. The firm will need to repay the shareholder for this transaction."

I don't know what was the question where you got that. These three statements seem to relate to increasing equity because of money to Bank; or, for instance, at year end, if you have a 3-person partnership, you would "close out" equity to allocate it to each partner's tracking account for their share of equity.

Look at your Title. You used the word "Contributed" but now, it turns out, that isn't what you meant? Contributions have to do with Charities.

The Business has Sales. Your bookkeeping system automatically "closes" income and expense each year to Equity for you. This is Net Income, in QB, and then it is seen as a change to Retained Earnings for the first date of the new year.

That has nothing to do with this: I want to get paid by the client, and leave it in the bank.

Fine. Leave it in the bank. But don't overlook that your Shareholder-Employee is Required to be paid, and paid through Payroll.

And an S Corp is a pass-through Entity. At the end of the year, the 1120S is prepared, the K-1 will be given to each shareholder who then reports the Taxable income on their 1040, even if no one ever took any money out of the Corporate bank. And again, the IRS requires Payroll.

And here's a common scenario I covered in my classroom:

At the end of the year, your Corporation has $100,000 in sales and that gives you $50,000 taxable reporting income. Meanwhile, you put $50,000 into that Building under construction. You still report on pay taxes on the income, even though you have no money in the bank.

Because Bank does not mean Income. It means Money. That's where you keep stating it oddly.