S-Corp or Schedule C for small biz

My wife is a hair stylist and she just started on her own after being in someone else's salon for years. It was time for a change and it's been terrific for her in so so many ways. 
Currently a schedule c business, our tax advisor suggested that she switch to an s corp to save a significant amount in taxes based on her calculations based on her current income and projected income. 
It's only my wife working At the salon and she has no employees. She rents a chair at a salon. Her overhead expenses are low. 
 

Can anyone give some advice in layman's terms?

When you are a sub-S corp, your corporate earnings flow through to your personal tax return and you pay one rate for the corporate earnings plus your personal earnings, in a single return; C-corp means the corporation is a separate entity/taxpayer, so the corporation files and pays taxes on its earnings, and then you also file and pay taxes on your personal earnings. Up to a certain size, sub-S makes sense because it's more streamlined, not a separate return, and the corporation is not large enough to take advantage of tax breaks. I would think your wife's business would be at the size where sub-S is the better choice..

Margie

I'm not up on the tax situation and I don't play a lawyer on TV, but I see a lot of smaller S corporations turning into LLCs.

Does that mean anything?

I would probably go with an LLC. It has the advantages of a Corp with the flexibility of a sole proprietorship. 

I've operated as a llc for almost 20 years. 

Is Sub S Corp is another filing type or is that anything smaller/ other than S corp?

Are you suggesting she look into a "Sub S Corp"? Is that the terminology?

Just so I know what else to look into. 

S-Corp and sub-S are the same thing. S-corp is probably the newer term.

Just a note on an s-corp, I am sure this doesnt matter, unlike a corp you need to be a citizen or resident to be able to be a shareholder/owner. 

Just thought I point it out. 

My understanding was that as a schedule C, you get hit twice for taxes, the corporate taxes for the company earnings, and then again on your personal income paid to you by the company (i.e. salary).

The S-corp with the pass through avoids the corporate earnings tax so you aren't paying taxes twice on the same income. 
 

Edit: I should have read Marjorie's answer more closely (since she already answered the question) and saved myself some typing. 

I'd recommend an S-corp since it's a small deal. The C-corp just adds more complexity - and expense - to the deal. As far as LLC vs. S-corp, that's a better question. There are pros and cons to both.

Schedule C is simple (personal 1040) sole proprietor pass-through taxation, not a C-corp. So the corporate double taxation and other C-corp stuff mentioned above need not apply.

Subchapter S corporation, shortens to sub-S corporation, shortens to S-corp.

Assuming you're just talking about LLC as sole proprieter vs LLC as S-corp for tax purposes, the main reason an accountant would be recommending filing as an S-corp is to reduce her self-employment taxes. This is done by paying herself a "reasonable salary" that reflect what somebody of her experience might otherwise get paid for similar work in a similar role as an in your area. A good baseline might be her pay rate at her former employer. I would think the simple chair rental would help reduce whatever additional might be needed to account for her being an 'owner' vs full-salon ownership. This reasonable salary is the amount that gets fully (income AND self-employment/payroll) taxed. Whatever she makes above that gets taxed at a lesser (income only, no self-employment/payroll) rate when it comes back as a "distribution". This does invite additional scrutiny from the IRS, looking for people going underpaying on their salary. There also might not be as much actual benefit if she's not making much (or any) more than before.

Another reason your accountant might be recommending filing as an s-corp is that your tax filing gets more complicated... And thus more expensive.