When you take a screenshot on recent versions of iOS, a small thumbnail of it will appear at the bottom of your screen before being saved to Photos.
You can tap this preview to open Apple’s Markup feature, which has a few tools to make edits and annotations. You can share the screenshot from Markup, then choose to save or delete it without having to dig into Photos.
If you just want to quickly share the screenshot, long-tap the thumbnail. The share sheet will appear whether you’re on the homescreen or in an app.