While both of the answers already provided here have some good insight I would like to share an arborists perspective. Palms are not really trees at all, but a kind of grass (at least from my professional perspective). The reason for this is that they are monocotyledons rather than dicotyledons. (this means that the seed only contains one embryonic leaf). Monocots are not capable of what we call ‘secondary growth’, but only primary growth. This means that they can only grow at the top where a true tree can gain girth and grow all over. This may seem false because obviously an ancient palm has a much thicker trunk than a seedling but it is the same number of cells, they have only swelled like a sponge. This is why a cross section of a palm has no growth rings, there is no true growth (by cell division) in the trunk. So for a palm there really only is one way to grow and that is up, where a tree as a self optimising organism may grow in all sorts of directions. This is also why if you cut the green top off a palm it is dead, where a tree will sprout a new top in time.

best :)