Achieving Consistent Behavior with Featured Images

After GOOGLEing this subj, I’m more confused than before. I don’t have years of experience with WP and the codebase, but I am a long-time software developer and know how to figure things out. But this is bedeviling !

What I have trouble with is: why don’t featured posts behave consistently, in that they might be displayed in thumbnail form to represent a blog post/page (usually, depending on the theme), the initial inline image for a blog post/page (again depending on the theme), is there a snippet of code I can manually insert to achieve consistent behavior regardless of the theme ? I’ve downloaded a few themes, set ’em up on a local WP installation, but I have to hand-off a site to non-tech users to have-at-it-on-their-own for their non-profit org’s website. The N-P’s Pres is managing basic edits/updates, but I haven;t discerned a rule-of-thumb for this subj, so far. I’ve showed them how to resize images (1080×810) to be well within the max image dimensions(4300×3300), yet I can’t figure out why featured images on blog posts on the home page are being cropped.

Anyway, suggestions are welcome. Good luck and thanx…