The homepage is the main page of the website or the application on which the user will land. In case of a website, the homepage is the main page which comes when user types in the URL of the website in the browser. For example: if someone types GOOGLE.COM the very first page which users will see is the HOMEPAGE.
If users enter any search term in the google search bar and the results of that search term will populate, this is the landing page. The homepage can be a landing page but a landing page can never be a home page.
The concept of landing pages are usually talked much in the SEO world where the PPC campaigns are run on landing pages which act as lead generation pages for the site/product.
In simple words of a website : the homepage of the website is obviously the home page and if the company has any product and when you click the product page it becomes the landing page of the product and similar to other pages.