You can create a story and publish it completetly on an iPad. Click that center icon at the bottom and it takes you to the editor. There you can type your story (not fun unless you have a bluetooth keyboard.)

Then you use the icons to format the title, subtitle, add images, etc. Unfortunately the Medium app doesn’t have Unsplash integration. You have to choose a photo from your Photos app. But you can download images from the Unsplash app (it’s free) directly to your Photos app.

Then hit Next and it will take you to the publish window where you can add tags, or submit to publications, or publish it on your own.

It is easier on a computer, but it is possible to use just an iPad (or iPhone.)