A website is typically made up of multiple web pages (5-20 pages for SME, in HTML format) while a landing page is typically a single-page webpage (in HTML format also).
A website is normally used to describe everything about your company or your business such as your company background, products, services, technologies, projects, team members, clients, partners, gallery of photos and video, FAQ, SOP, resources, manuals/leaflets/user guides for download, and contacts. As a website can contain many pages, many hyperlinks and a lot of information, your customers may lose focus or get lost easily while they navigate your website.
Whereas a landing page is much simpler as it is only one page, typically used to do marketing or promotion for one product or one service or one special offer. The presentation of materials in the landing page is sequential, you browse from top to the bottom of the page. At the end of the page, you only get the customer's focus to do only one thing, may be to fill up a webform for their contacts, or click a button to place order or sign up for something. It is said that a landing page is much more effective in network marketing than a website.