'In any case' can mean 'whatever happens', 'whatever happened', 'regardless'. For example: 'in any case, I will definitely still buy the house' or 'in any case, it's not important'. 'In that case' means 'because of that', 'seeing as that's going to happen'. For example: 'oh! You're not coming home until 6? In that case I won't prepare any lunch for you' or 'I heard he lost his job...in that case I wouldn't buy a new house!'

We use "in that case" when we have to take a certain coyrse of action or change plans because of outside circumstances. For example: 1. It is raining .... In that case I will take my umbrella. 2. I didn't eat breakfast ... In that case we will have an early lunch We use "in any case" when events do not have an impact 1. It is raining but, in any case, we will go out. 2. I didn't eat breakfast but, in any case, we will have love at 1pm.