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Well,when talking business you're mainly talking about an interface that is simple and fairly intuitive,opposed to the approach of a personal interface which is customized for one,unique user (you could say "tailored as a suit").
Now,for a more precise explanation and a better comparison,let's take this matter step by step...
Firstly,as i already mentioned,the target users are completely different.On a business interface you have a basic user or (quite often) a user that hates computers and doesn't like working with them,or (worse) a user that never worked with a computer. This requires a simple interface that is intuitive and doesn't make these two users cry or go mad (although it's fun watching their reactions.....).
Also,the interface will need to obey to the trend that already exists on the market (color schemes,displacement of the buttons,the text written on the buttons,sounds emitted on click),if this already is there and if it's not rubbish (most of the time it is rubbish,sadly) and also (most importantly !!!) if the future user doesn't ask for a interface that is already existent (take the Windows vs Linux vs Mac case...).
When talking about customized interface,you already know you're dealing with a user that knows his/her stuff. A customized interface usually is made with the specific purpose of maximizing production (or because you get annoyed by the dysfunctionality of the basic interface). Moreover,a customized interface means there are no limits ( YOU CAN CHANGE EVERYTHING.....YAY !!!) to what you can do. Also, the public these two interfaces are targeted at is fundamentally different. Firstly you,ve got the bold,money interested business people,who maybe don't like technology , and then you have the computer user with a 7 year old imagination that wants to play , and he/she's not affraid of messing around with the console in Linux,for example (actually,these kind of people enjoy this kind of stuff....i can tell since i'm one of those crazy 7 years old minded people....!!!!!!!!!!!). Hope i answered your question ! Message me if you have any other curiosities regarding interfaces,or if you need a wild imagination for an interface design !!!!
Oh,forgot to talk about approaches in the design......
In corporate interface design you usually ask people what they want ,you make statistisc( boring stuff....),more design options that you ask them to choose from and you're basically asking other people to tell you what they want...(just like a waiter in a restaurant who takes an order from a client).
On a custom interface design you can go mad,do all the stuff you like,or try stuff until you're comfortable with it (this time you're the crazy client that tied the waiter to the chair and went in the kitchen to fire the chef and cook his own meal..... ).