The Kingdom of Heaven vs the Kingdom of God

There are people who believe the Kingdom of Heaven talked about in Matthew and the Kingdom of God talked about in Mark & Luke are different things.

I don't believe that is the case.  To make the point, let's look at Matthew 13:31-33 and Mark 4:30-32

Matthew 13:31-33 reads...

Here is another illustration Jesus used: “The Kingdom of Heaven is like a mustard seed planted in a field.  It is the smallest of all seeds, but it becomes the largest of garden plants; it grows into a tree, and birds come and make nests in its branches.”

Mark 4:30-32 reads:

Again he said, "What shall we say the kingdom of God is like, or what parable shall we use to describe it? It is like a mustard seed, which is the smallest seed you plant in the ground. Yet when planted, it grows and becomes the largest of all garden plants, with such big branches that the birds of the air can perch in its shade."

Luke 13:18 reads quite similarly to Mark. So why the different phrase?  It is the audience that the different books are written to.  Matthew was writing to a primarily 1st century Jewish audience.  They would have been offended if he referred to God in a too casual way so, in tradition, there was an inference of God by saying Heaven.  Mark and Luke were writing to a primarily non-Jewish audience.  One not offended by the use of God in that context.  I don't know but they may have been confused if "Kingdom of Heaven"were used instead.