Probably correct. Although it isn't really relevant for your site.
A landing page is a page user sees when coming to the site from somewhere else. Typically this a special page shown on first visit or when coming from a specific source such as an advertising campaign. The main point here is to show the user the info relevant to the reason you think he is on the site without extra interface clutter. Basically show the user that this is the site he wants and why. And a direct access to what you think he wants to do or what you want him to do. I don't think there is any point using the term for a login page, just think of it as login page, but it is probably accurate enough in this case, since your site is that simple.
A home page is the default page of the site. The place you from a landing page when you "enter the site" or from an error page when you "return to the site" or, yes, from the site logo when you are on the site. A site could have different subsites with their own homepages. Generally it is also the page that is returned when you type just the domain name as address, but it could redirect to a landing page or login page under certain conditions. It is related to the logical structure of the site and since there is no hard limit on how messed up or complex that can be, there might not always be a simple way to spot the homepage.