Inbound Marketing - creating front end marketing pieces to bring leads to your business to sort, follow up with, and close. Ideal for highly systematized business with similar deliverables. Generally the method utilized in the classic approach to providing services.
Inbound marketing faces the unique challenge of trying to find the right kinds of clients, you're reliant on your marketing efforts to attract your perfect client avatar; good for systematized businesses; bad for boutique types of services.
Outbound Marketing - using front end marketing pieces to establish authority while actively seeking out prefered client types and soliciting them for your services. Akin to Direct Marketing and cold calling.