Compare these two handstands. They’re a prime example of the difference between an arched handstand and a straight handstand.
The most notable difference is that the straight handstand features a greater (more “open”) angle between the shoulders and the chest, so requires more flexibility. In the arched handstand, however, the “closed” shoulder angle necessitates that the back must arch in order to get the legs (and therefore the body mass) directly centred over the hands. The wrists are also often extended back lot more in the arched handstand to try get more body mass over the hands.
Because the handstand is most difficult to balance in the front-to-back direction, an arched back makes it easier by allowing you to control your balance by altering how much you arch. A straight handstand, however, can only be controlled at the wrist. Therefore the straight handstand is a prerequisite for more difficult hand-balancing positions (like one-arm handstands), and also scores higher in gymnastics than the arched handstand.