Some clarifications are needed to fully understand why some fruits come true and others don't. Let's get some basic ideas straight. Self fertility and self incompatibility are not absolutes, but are a scale, with various fruit varieties somewhere on a line between the end points. With apples as our example, they would be more on the self incompatible side. A few varieties are self fertile enough so that you can get some fruit from self fertilization, but will do much better with cross pollination. Notice that I said self fertilization, as there are no apple trees (and no other fruits that I know of) that self pollinate. Bees pollinate apple trees, even ones that are self fertile, so if you see a claim by a nursery that a certain variety is "self pollinating," you have a reason to shop elsewhere with nurseries that know their own business better.
To pollinate is to move the pollen, either from anther to stigma on a self fertile plant, or between flowers in cross pollination. To pollenize is to provide viable pollen for fertilization to occur. In street language, it's the difference between the pimp and the john.
Thus an apple tree might self pollenize, if it is self fertile, but it cannot self pollinate. Nor can an apple tree pollinate another apple tree - bees do that. But an apple tree can pollenize another variety. Apple mates are called pollenizers. In most commercial orchards today, crab apples are the pollenizers of choice, because 1) they produce abundant and fertile pollen, and 2) the pickers cannot get mixed up and put the pollenzer fruit in the bin.
This means that, if you plant seeds from a supermarket, the odds are that you will eventually (seedlings take a long time to fruit) get a cross between the variety you ate, and a crab apple. This is not a very good formula for growing quality apples. If you want to cross two varieties, you might choose an apple fruit that's grown with only two varieties and no other apples in the neighborhood. Or you might hand pollinate to make a deliberate cross, then bag the blossom to make sure of no contamination from other pollens.
If you want to grow fruit from seed, your best bet is to choose fruits that are self fertile and do not need pollenizers. Good examples of these are peaches, sour cherries and most citrus, which are all high on the self fertility scale. There are no absolutes here, only odds.
If you grow seedlings from fruit that is high on the self incompatibility scale, such as apples, sweet cherries, some plum varieties, etc., your chances of getting a fruit that is true to the one you ate become very small. You will (almost 100% odds) get a fruit that is a cross between your fruit and the pollenizer that was present at bloom.
We need to understand that most temperate zone tree fruits are usually grafted, so a block of say, Red Delicious, is for pollination purposes, all the same tree. So planting such a block, without pollenizers would be serious misjudgement. I've seen people do this, however. Then they have a problem, which must be corrected.
Growing fruits from seed is an endeavor for the young who have lots of land, or for a teacher who wishes to illustrate. Seedling trees take much longer to bear fruit than grafted trees, and you lose all the benefits of the rootstock. For me, I am old, and my space is limited, so I will graft my apple trees. I generally get fruit in the second year, as opposed to the 8-10 years that is typical of seedling apples. I also will never fall off a 25-foot ladder while picking. All my apples require no more than one step up to reach.