as to what's a significant difference is, there is no hard definition. if your home has an old outdated interior the rent would be less than an identical house next door that has been modernized. you call in 3 realtors to appraise what your property should rent for and you're going to get 3 different values. Zillow is not a real estate company so between their estimate and a realtor, whose judgment do you think a court would give more weight to.
I've seen IRS rulings where 80% of FMV is okay. So it depends upon what percent the $400 represents. So $1600 v. $2000 (luxury apt) is probably okay, while $600 v. $1000 probably isn't.
It largely boils down to WHY you are charging that amount you charge.
Why are you charging your tenants $400 less than other properties in the area? It depends on the facts-and-circumstances.
HUD has a website where you can look up fair market rentals for a given location. Here's a link:
As @Mike9241 said, the IRS does not have a clearcut rule on this, but obviously the further your rent is below FMV, the more likely it is that your return gets questioned.
There are court cases that accepted 80%, and there are court cases that didn't.
There is no clear cut definition of "Fair Market Rental Value." The best I can come up with is this:
What the consumer is willing to pay
What others charge for a "SIMILAR" property in your area has only a little to do with it. If there's an identical 3br/2ba house next to yours that gets $1000/mo, but you're only charging and collecting $600/mo, the question is why?
If the property next door has been modernized with new appliances, more energy efficient windows and a new roof, and yours has not, then that could be why. So in this situation, are you charging FMRV? Most likely yes.
It's all very subjective. The FMRV question mainly comes into play based on two criteria, with the main one being, "are you renting to a family member?" (there are other criteria, but I'm not addressing that here.)
The other question is, are you renting with the intent to make a profit?
I would recommend looking at other sources for determining your FMV, and this would be more of a question if you were charging mush more than what other renters in your area are charging for a house or Apt. Value should be fair and reasonable, what someone is willing to pay, and what you are ok with, financially.