A "reward" in the Bible represents something that brings people together, or brings spiritual states together, and binds them. In the Bible, of course -- especially the New Testament -- we're told repeatedly to do what is good and right "without thought of reward." That's because removing the idea of a natural reward lets us be aware of spiritual rewards, which are actually intrinsic to the good that's being done. On a relatively low level, we feel delight in doing something nice and useful for someone else; that delight is a reward. The love that can exist between partners in a committed, loving marriage is a reward. The delight we feel when we truly want what is good and know how to create it is a reward. And ultimately, our conjunction with the Lord and the delight of His love and salvation is the deepest reward of all. These are the things meant when the Bible speaks of "rewards.

A "house" is essentially a container -- for a person, a family, several families or even a large group with shared interests (think of the term "houses of worship.") In the Bible, a "house" is also a container, but for spiritual things rather than natural things. In various uses a "house" can represent part of the mind, the whole mind, a whole person or even a church. The other nuance to the word "house" is that it is generally used in regards to our affections and desires rather than our thoughts and principles. This makes sense; we tend to engage our thoughts and rationality when we are out in the world doing our work, but when we are inside our houses we are driven most by love for our families and the desire to be good to those we love. So "house" tends to represent the things we want and care about -- which are ultimately the things that define us.