No, this is Not Correct: "But if it is included in W-2, I feel it is the same to deduct in either S-corp or 1040 because S-corp will flow through shareholder in the end(if the client is the only shareholder of the S-Corp). Is that correct?"

The IRS has many things they investigate and watch for. In general, that would be Transferring personal costs to a business, which is Prohibited. That's why it is taxable as a Fringe Benefit through Payroll, for Social Security and Medicare, but not for Income tax. The shareholder then, Personally, puts it as an allowed deduction on their 1040. That helps you understand why it isn't part of Income Tax Withholding on the W2, although some employers don't bother to skip that part.

"Is health insurance included in Box 12 of W-2 with code DD?"

Did you look that up for yourself? Google this:

w2 box 12 codes dd

And bookmark the result that gives you clarity, for future needs. Build your resources. Here's another:

https://www.irs.gov/businesses/small-businesses-self-employed/s-corporation-compensation-and-medical...

"If the client is the only owner of S-Corp, what is the difference between deducting in C-Corp and Form 1040? S-Corp will flow through the shareholder in the end."

Because you are explaining that there is an intent to use the Business to take personal expenses as if that is part of the business. It is disallowed. That why you would not do this.

And because you keep overlooking that it will show for the business as part of Gross Taxable Fringe Benefit as part of the labor cost deduction. It cannot also be health premium expense deduction for the Business.

When the business pays the premium for a "more than 2% shareholder" they need to Tax it through Payroll as a Fringe Benefit. The fact that there is a personal provision for that shareholder to include it as part of Deductions is because, as the employee-shareholder, they are quasi- "Self-employed." It has the special treatment of not being business deduction as Health Insurance, as would be true for "non-owner" employees, and it has the special provision that the Shareholder-employee gets to deduct it on the 1404, but a "non-owner" employee does not. If there are shareholder-employees, there are different rules.

For a C Corp, you cannot compare to S Corp. The rules are different, yet.

Are you taking continuing ed classes, webinars, workshops, etc to stay current on tax regulations? Because this one changed for S Corps over 10 years ago.