Leadership styles and skills are two very different things that come into play when leading people. Everyone who leads has a leadership style—it is the manner in which they tend to lead, typically related to personality traits. A leadership style can be strict or laidback, informal, delegating, or any number of different types of leading others.
Leadership skills, however, are an individual’s natural capacity and propensity towards leading. If someone is charismatic, driven, and engaging, they are better at leading naturally, so these are leadership skills. Someone can improve their leadership skills through practice and concerted effort (by working on their speaking, trying to be more amiable or severe, etc.). Leadership skills are beneficial to being an effective leader, but everyone will have a leadership style.