Randyman,
Nick gives good advice on how to propagate a Sweetgum from seed. You mentioned, however, that one tree had brilliant red foliage, the other duller. Be careful in thinking because you harvested a fruit from the brilliant red tree, that you will get a tree with similar foliage from a seed from that fruit.
Trees are highly genetically variable, especially Sweetgums. The genes of both parents during sexual reproduction of a genetically variable organism will assort independently during meiosis, and when the gamete (what will become the egg and grow into the tree) is formed from this random mixing of genes, the eventual characteristics of this tree, such as leaf color, vigor, resistance to disease, etc., will entirely be determined by chance. In other words, if you plant 20 seeds from your Sweetgum fruit from the brilliant red tree, you will get a range of seedlings that display leaf color from red to dull.
But you will probably not get brilliant red, because that particular tree is most likely a clone – grafted on a hardy rootstock – that came from an exceedingly rare seedling (or sapling) that was spotted by a wary nurseryman. He or she then tested it for other desirable characteristics, and after meeting most of these criteria, it became part of the nursery trade. Probably thousands of trees grown from that one clone, now manifest themselves as beautiful trees across the North American landscape.
So, the only way to get a tree just like the one you like is to clone it – thus keeping the exact same genes as the parent. In the case of the Sweetgum, you can either do it by making softwood cuttings, by grafting or budding, or by layering.
The other way to get the brilliant red color, is to grow the seeds en masse. Among hundreds of seedlings, you are bound to get one with the characteristic you’re looking for. Most likely you won't want to do this, but it was the way the most famous plant “breeder” of all time developed his unique plants.
Luther Burbank rarely bred (crossed or hybridized) plants. He simply allowed a particular plant to become pollinated naturally (randomly), planted thousands of the genetically variable seeds on acres of land, then when they grew to seedlings, he selected the unusual ones that held potential. Luther Burbank’s genius was the ability to spot the “specialness" of an adult plant when it was a mere seedling.
My favorite Luther discovery: McDonald’s French Fries!