Cherry Blossom... are they all actually cherry trees?

The cherry trees involved in these displays are mostly a non-fruiting type. These are the ones planted along roadways, and in botanic gardens to create that early spring display of blossoms. But yes, when someone says "cherry" blossoms, they mean a cherry tree. These usually bloom long before other fruit trees, which is why they're considered such an important sign of spring. 

Yes and no.

The sweet cherry we eat is Prunus avium, and the sour cherry Prunus cerasus.

There are well over a dozen different species of cherry, however, and the trees grown for their blossoms are other types of cherry, most often Prunus serrulata and Prunus speciosa, but there are a dozen or so species used in total. 

Varieties with double flowers (that is, flowers with multiple rows of petals, rather than the usual one) will not produce fruit, as they are sterile. Inter-specific hybrids (produced by crossing two different Prunus species) are also usually sterile so will not produce fruit. 

All other flowering cherries will produce fruit, but they are not eating cherries, and the fruit they produce are small, bitter and usually not fit for human consumption (some are even poisonous). 

So basically, most flowering cherries will not produce the sort of cherries you are used to seeing (many will not produce fruit at all), but they are still legitimately cherry trees, not some other type of flowering tree. 

Cherry blossom festivals and such mean actual cherry trees.

It's supposed to mean blossoms on cherry trees. If people are using 'cherry blossom' to describe blossoms on some other kind of tree, then they are describing them incorrectly. Not all cherry trees produce cherries, or at least not cherries that are used for food, they being too small or too bitter or something else that makes them not useful as food. The ones that don't produce cherries for eating are called ornamental trees, prized for the blossoms but not the fruit.

They are talking about the 100's of different types of cherry tree's. The one in my  yard has not started blooming as of yet, but my apple has.  That is backwards for how it normally works.

All fruit tres flower, cherries, plums, etc. not all go to fruit, they are ornamental.. almonds and walnut trees also flower