Link category is asking how relevant or related is the website that is linking to your site.
Identical to my site means that the website where your link is going to be placed is exactly the same category as your website. For example, if you have a real estate website a link from exactly the same category would have to come from another real estate website.
Similar to my site means that the category of the site where your link will be placed is not exactly the same as your site but is a similar category. For example, if you have a real estate website a similar category could be a mortgage website.
Not related to my site is a link from a website that is not related to yours in any way. For example, if you have a real estate website and the link is from a shopping site that sells facial cream.
General/Web Directory is a link from a site that has multiple categories in it like a web directory.