Using "Log in" vs. "Login"
Login, spelled as one word, is only a noun or an adjective. For example, the information you use to sign in to your email is your login (noun), and the page where you sign in is the login page (adjective). 
Log in is two words when it functions as a verb. For example, you log in with your login information.

Using "Checkout vs. Check out"
Checkout is a noun and an adjective. The corresponding verb is two words—check out. For example, when you are ready to check out at the grocery store, you wait in the checkout line. Or when you want to check out of your hotel after the standard time, you might ask for a late checkout.