Now, I have managed to create a post with both the styles of attachments. I assure you, this was not planned!
Interestingly, all 4 attachments were uploaded using the same method. However, the one shown in the "Attachments" box at the base of the post was the only one not posted in the composition of my post. ( Gawd, this is sounding complicated, doesn't it?!
I am sure it isn't as complicated as I am making it sound...)