expandtab affects what happens when you press the <TAB> key.

• If expandtab is set, pressing the <TAB> key will always insert softtabstop amount of space characters.
• Otherwise, the amount of spaces inserted is minimized by using TAB characters.

shiftwidth affects what happens when you press », « or ==.

• It also affects how automatic indentation works.

softtabstop affects what happens when you press the <TAB> or <BS> keys.

• Its default value is the same as the value of tabstop, but when using indentation without hard tabs or mixed indentation, you want to set it to the same value as shiftwidth.
• If expandtab is unset, and tabstop is different from softtabstop, the <TAB> key will minimize the amount of spaces inserted by using multiples of TAB characters.
  • For instance, if tabstop is 8, and the amount of consecutive space inserted is 20, two TAB characters and four spaces will be used.

tabstop changes the width of the TAB character, plain and simple.