Insert image is just inserting image into The "Attach this ....." -box is if you have an Inside link to a pic that needs to be attach (If you don't the reciever cant view it)

And you don't tick it when you use an outside link and don't want to increase your mail with a copy of that. (see pic)

I have all "inside" links, if you mean pix on my computer's hard drive. I'm not sure what your pic is showing me, so, sorry, I have to click the 'not helpful' box in this case. I'm reporting a function that used to work, but no longer works. Is it a local problem, or has Thunderbird changed the "Attach" function's to mean something else? I'm using ver 38.3.0.

I can't remember it ever working different, If it did work as you describe there would be no difference between insert and attach. You have the "attach" pull-down and the insert-icon

My pic was to show you the resulting mail-source when not marking the "attach this image to the message" -box in insert a pic. There is a line moz-do-not-send=true. The link is to a public-image so there is no need to include the whole 1.8MB in the message. Useful if you can place pics on a server and want to share them with many.

If you want another way of attaching files use Ctrl+Shift+A

Just to clarify, your pic will be a part of the message IF you pic that box. An inserted pic is not presented as an attachment.