I think it is pretty clear from the link you added: if you use @CheckForNull and the code that uses the value does not check for null, FindBugs will show it as an error.
FindBugs will ignore @Nullable.
In practice this annotation is useful only for overriding an overarching NonNull annotation.
Use @CheckForNull in the cases when the value must always be checked. Use @Nullable where null might be OK.
EDIT: it seems that @CheckForNull is not well supported at the moment, so I suggest avoiding it and using @NonNull (also see Which @NotNull Java annotation should I use?). 
Another idea would be to get in touch directly with the FindBugs developers, and ask their opinion about the inconsistency in the documentation.