Updated September 29th, 2020.
The Mac Mail app shows all attachments as icons– unless the attachment is a single-page PDF or image. For example, if you attach a Word document to an email, it shows up as an icon.

If you attach a Pages document to an email it’s the same thing: an icon.

If you attach a sound file, or a movie, or an Excel spreadsheet, or a text file, it shows up as an icon.
But… if you attach a single-page image, or a single-page PDF, you will see the attachment “in place” in the body of the Mail message (that is, it won’t be an icon– it will show the actual image). Like this:
The key is “single-page.” All of the standard graphics formats are single-page: JPEG, PNG, TIFF, BMP, PSD– all single-page. Any attachment in one of those formats will display the attachment in line.
PDFs are the one tricky case because a PDF can be multi-page. The rule is, if the PDF is one page, it’s going to show up “in place,” but if it’s multi-page, it’s going to show up as an icon.
Here’s an email with a single-page PDF attached:
Here’s an email with a multi-page PDF attached (it’s a book):
How to make your single-page images and PDFs display as icons
If you want a single-page image attachment or a single-page PDF attachment to appear as an icon rather than “in place” just control-click on the attachment (after you’ve attached them) and choose “View as icon.”
Then your email looks like this:
(This is the Mail message we saw previously, with the deer picture in it. Now the image is an icon.)
If you change your mind just control-click on the icon and select “View in Place.”

Note: none of this matters to the recipient. It’s all for your benefit. When you send an email you can control how it looks to YOU but you can’t control how it looks to the recipient. Some email programs are set up to show attachments as icons no matter what. Some email programs are set to show attachments “in place” if the attachment is a single page image. Some offer a choice. You, the sender, don’t control how things look to the recipient. Something to keep in mind!
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Sounds good, but when the email with one page image reaches the recipient the “view as icon” instruction is no longer valid and the image shows “in place”. Very messy.
Correct, assuming the person is using an email program that chooses to do it that way. In the end, what you do at your end with an email doesn’t define what happens at the other end.