Hello Steve.
Yes, web parts and widgets placed in zone managed by
CMS Editor are bound to page template, so it is like you said. When you do some change on given page template, it is reflected on all pages based on this page template.
If you want to make it independent, so you can have different web part or properties, you need to clone given template as ad-hoc template. Or you can use editable web parts, like
Editable text or
Editable image. Content of these web parts (as you can set in on Page tab) is bound to page, not page template, so it is independent even when using the same page template (content, not web part properties).
Second option is to drive web part properties via custom macro, ad you can set their value dynamically in code. Anyway, if your goal is to change text and images, you can consider using of editable web part, like I mentioned. Thank you.
Best Regards,
Radek Macalik