It is possible to share a link to an individual padlet post.
Here is an example of a hyperlink to one of the 39 posts on my Remake of Roald Dahl Padlet.
I have changed the Privacy Settings to allow anyone to view the Padlet by clicking on 'Share' and changing the Privacy Settings to Public, Visitor Permissions: Can Read.
Click on the ... button of the post then Expand Post to view the URL. Copy and paste the link into any message, post or comment. You should be able to view the post by clicking on the hyperlink below.
https://padlet.com/stebridgwater35/fneppm2i0gd6f6wo/wish/922585468
To embed a padlet on your blog or website, you will need to click the Share button that is located at the top-right of the screen. A list of options will appear. Click on 'Embed in Your Blog or Website' for the HTML code that you can copy and paste into your text editor of your blog or your website. To learn how to embed Padlets in different platforms visit the support Padlet to discover more Embed codes for other websites and platforms. The link to this Padlet is: https://padlet.com/support/embed
If you are using an LMS, like Canvas, etc., I believe by integrating a Padlet into your LMS, you can turn a feature on so that each student gets their own copy of the Padlet.Instructions here. There may be an easier way, but I've never run across one. Best of luck.