#Yes, the jump is the distance from the ground to the bottom of your feet
Yes, the jump is the distance from the ground to the bottom of your feet
When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier [...] Either way, each foot you clear on the jump costs a foot of movement.
Intuitively, a vertical jumping distance makes the most sense as the distance between your shoes and the ground but really your entire body is moving the same distance upwards. The rules' language talks of the distance you "clear" and "leaping into the air" both of which evokes the imagery of the gap between ground and shoes. More direct evidence can be found in the following passage:
You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1 1/2 times your height.
So it is clear from the rules that when you jump, the distance is measured from the ground to your feet and that means that the rest of your body moved vertically that same distance.
###If the PC can jump X feet, their feet reach X feet
If the PC can jump X feet, their feet reach X feet
If a 6' tall character jumps up 8' it means that their feet are 8' above the ground and their head is 6' + 8' = 14' above the ground. If they raise their arms the tips of their fingers would be 1.5 * 6' + 8' = 17' feet above the ground.
In this case, if a character jumps up at a 8' wall with a jump of 8', then the assumption is that they land on their feet on top of the wall.
###The way the jump looks narratively is not defined
The way the jump looks narratively is not defined
How all this jumping and leaping looks is completely situational and also not at all defined in the rules. In cases like these, the DM must fill in the blanks.