From the official jQuery documentation

• .mouseover()
  Bind an event handler to the “mouseover” JavaScript event, or trigger
  that event on an element.

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• .hover() Bind one or two handlers
  to the matched elements, to be executed when the mouse pointer
  enters and leaves the elements.

  Calling $(selector).hover(handlerIn, handlerOut) is shorthand for:
  $(selector).mouseenter(handlerIn).mouseleave(handlerOut);

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• .mouseenter()

  Bind an event handler to be fired when the mouse enters an element,
  or trigger that handler on an element.

  mouseover fires when the pointer moves into the child element as
  well, while mouseenter fires only when the pointer moves into the
  bound element.

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What this means

Because of this, .mouseover() is not the same as .hover(), for the same reason .mouseover() is not the same as .mouseenter().

$('selector').mouseover(over_function) // may fire multiple times

// enter and exit functions only called once per element per entry and exit
$('selector').hover(enter_function, exit_function)