Fathah shows the upward movement of that letter on which it sits

dammah ضمَّة is a small "و" wow sign sitting above the letter, causing no movement.

Kasrah sits above the letter to make it move downwards.

Shaddah, our happy tale bear buddy, it makes a shaddah combination in which it attaches previous letter with the next letter of word.
The direction of movement will depend on the harkah seen on it.

The shaddah means two same letters together.
Out of these 2,
first letter is with sukoon and second letter with the showed direction of movement (haraka) on it,
It can be any one out of dammah, kasrah and fathah.

sukoon is the most peaceful haraka among all, it prefers to rest and give no movements.

fathah tanween sits above the letter as fathah and gives us a sound of "un"

Dammah tanween sits above the letter as dammah and gives us a sound of "un"

Fathah tanween will give same sound as kasrah tanween, just the difference comes when dammah tanween is used.

Short vowels in Arabic are basic signs over letters.
These harakat are giving life to these letters, as the movement it gives to letter is sign of life.
Formula of Word = letters + their harakat