Presumably this small difference: Jaký mají dům? - What kind of house do they have? Jaký je její dům? - What is their house like?
Nope it is not the same thing in English. And it has a different Czech translation, that is "Který dům mají?".
What do you think is the difference between my answer, "How is their house?" and yours, "What is their house like"?
"How is their house?" is asking about the condition of the house. It is like you might ask, "How is their son?" if you knew he had been ill and wanted to know how he is doing now. "How is their house?" might be used, for example, if you knew there had been a hurricane in the area where the house is. You would use it, In this case, because you want to know if the house was damaged in the storm, and what condition it is in now.
One the other hand, "Jaký mají dům / What kind of house do they have? / What is their house like?" is asking for the descriptive characteristics of the house: Is it a townhouse or a single-family home? What is it made of? What color is it? How many floors/rooms does it have?