Form 433-D vs. Form 9465

"I was unable to find similar wording on the IRS website."

It's just setting up the payment. The text for this is all over the IRS, but in various places and steps.

"It is only when your information has been reviewed and approved that you can finally fill out and submit IRS 433-D."

From: https://silvertaxgroup.com/guide-433-d-installment-agreement/

"I’ve never had a client tell me that they received a form 433-D from the IRS in order to complete their installment plan."

It is for that specific payment method. if they don't want to do it that way, don't use that form.

Have you read the various 433- instructions? An installment plan, how to submit for it, and the fees involved will vary depending on business or personal, amount owed, and how it is or is to be paid. Also, if the person applies for any waivers or forgiveness, such as being below the poverty line. And the various application methods carry differing fees. You typically want to use the least expensive application and payment processes, if you can do so. And that's why you use 433-D. The 433-D is the Payment details; it reduces the fees if using this method.

From: https://www.irs.gov/payments/payment-plans-installment-agreements#costs

What are payment plan costs and fees?

If the IRS approves your payment plan (installment agreement), one of the following fees will be added to your tax bill. Changes to user fees are effective for installment agreements entered into on or after April 10, 2018. For individuals, balances over $25,000 must be paid by Direct Debit. For businesses, balances over $10,000 must be paid by Direct Debit.

Apply online through the Online Payment Agreement tool or apply by phone or by mail by submitting Form 9465, Installment Agreement Request.

Note: If making a debit/credit card payment, processing fees apply. Processing fees go to a payment processor and limits apply.