What you are describing is the expected behavior of a program of this type. When you "save" a document, it saves it in the native Affinity Photo format, with an extension of .afphoto. It keeps the window open so you can continue to make changes if you want. If your question is how do you produce something other than a .afphoto image file, you have to "Export" the image. Under Export you will see various choices such as jpeg, tiff, psd, png, etc.
Just realized after reading another post, the above is not 100% accurate. If you open a jpg and make changes that fall within the scope of what is allowable for a jpg, the save option actually overwrites the original jpg instead of creating a .afphoto file. But, if you add a layer to the jpg while editing, the save will be in the .afphoto format. Not sure I like this behavior, would prefer if it were consistent.