I don t think you are explaining your problem clearly.
You are clicking the thumbnails on the homepage and that takes you to the post, then on the post page you also see the thumbnail and it is clickable? Is that it?
Here is what you are doing wrong: When you are adding a Featured image, after your uploaded the image, click on the link that says "Use as featured image" then "save all changes" and nothing else. I think that what you are doing is after you uploaded the Featured image you are also adding it as an image in the post and are probably clicking the "insert into post" button. Try again without "insert into post" and you should have that featured image only show as a thumbnail on the homepage and NOT on the page itself.
Does that help?