#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 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 you jump up 8 feet then your feet are 8 feet above the ground and your head is [your height] + 8 feet above the ground. If you raise your arms the tips of your fingers would be 1.5 * [your height] + 8 feet above the ground.
###If the PC rolls a number, that is the distance their body reaches
The whole point of having jumping rules is to allow a character to be able to jump and presumably reach areas that are higher up. If a jump roll comes out to 8 feet, it makes no sense to then not allow that character to scurry onto/over the 8 foot tall ledge/wall/hot dog stand. If getting 8 feet on my jump check does not mean that my character can physically get to that area 8 feet up, then it is meaningless.
In this case, if a character jumps up at a 8 foot wall and gets a jump of 8 feet, then the assumption is that they jump neatly on top of the wall landing on their feet.
###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.