Theme’s page.php and index.php template files are confusing me

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WordPress Template Hierarchy:

You should read about WordPress template hierarchy.

This question also has some related answers.

Typical Case:

In your case, the most likely scenario is:

The explainer had set the latest posts as the home page (this is the default option) and you have set a static front page as home page. Since his is blog archive, it’s being loaded by index.php and yours is a page, so that’s being loaded by page.php.

This is just a typical scenario, but there may be other settings that are affecting which template file is being loaded.

Changing the default setting:

If the above is your scenario, then changing the following setting from WordPress wp-admin -> Settings -> Reading -> Your latest posts (then Save Changes) will make it the same for you and the explainer. Check the screenshot below:

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