Public access means that anyone can open your story map if they can find it, for example by searching ArcGIS Online or doing a Google search (especially that includes ArcGIS as a search keyword). If a story map contains sensitive or private info that you don't want everyone to be able to see, don't share it publicly. If you want to share a story map with a few people privately, for example so they can review the work, then there are several ways to accomplish that, the easiest probably being adding view-only accounts for them on your ArcGIS Organization so they can sign in and view the story, if it is shared just inside the Organization.
Here's a handy blog post about sharing and findability:
> Managing Security and Findability of Items with the ArcGIS Sharing Model
https://www.esri.com/arcgis-blog/products/arcgis-online/sharing-collaboration/managing-security-and-...
and there are some more useful posts on the ArcGIS blog if you search for sharing in ArcGIS Online: You searched for | ArcGIS Blog
For content that isn't sensitive or private, it is usually not problematic to share it publicly if that helps you do your project. For example, you may be working on a story map that will be shared publicly and launched as part of an upcoming initiative or campaign, but you want to be able to share it with a bunch of people, such as stakeholders or collaborators, to review it before the actual launch date. In this case, authors often just go ahead and share the story publicly. We often do that ourselves in our team too when we are working on stories with third parties or want to make it very easy for people to see a draft story. However to protect yourself in this situation, the best practice is to add some wording like Draft, Do not share, into the title of your story and also into the brief summary text with which it is documented in ArcGIS Online (the title and brief summary show up when people do searches in ArcGIS Online, like this search for all Story Map Journals). This will signal to anyone who finds your story that it isn't ready to be promoted or shared widely yet (some over-eager Story Map team members, namely me, have been known to jump the gun after finding great new stories in ArcGIS Online that were shared publicly for easy review but not officially launched yet). So it helps to add some text about draft status if you share something publicly before it 'goes live'.
The other end of the stick with this is when you do go live with a story you have created, how do people find it once you have made it public? Just making a story map public (or any map or app) in ArcGIS Online doesn't mean that the intended audience you created it for are going to be able to find it. Your audience are not likely to be ArcGIS users or know anything about ArcGIS. So making a story map public isn't the end of your work: it's up to you to promote your story and get it in front of your audience. A recommended way to do that is to put a link to your story map into the most relevant web page on your website. You could alternatively embed your story map into that web page. The Story Maps Gallery contains some examples of linked and embedded stories so you can see how other authors are doing this. This makes sure that people browsing or searching for the subject of your story will find it, not by finding its entry in ArcGIS Online, but by finding the page on your website that features the story map. And of course, sharing your story map (or any public map or app you create with ArcGIS) on social media, email newsletters, etc is also a good way to get your message out, just like with anything else on the web.
Hope that helps
Rupert
