Short answer
Every Shopify storefront publishes its theme details in the page source. Open the store, view the page source and search for Shopify.theme. The schema_name is the theme's real name, schema_version is its version, and a theme_store_id means it came from the Shopify Theme Store. A free detector reads all of it for you.
Free tool for this
The quick way
Enter the store's address into a Shopify theme detector. It reads the public page and shows the theme name, its version and whether it came from the Shopify Theme Store. It takes a few seconds and does not need a login.
How to do it by hand
Open the store's homepage. View the page source: Ctrl+U on Windows, Cmd+Option+U on a Mac. Search the source for Shopify.theme. You will find a short block of settings with the theme's details.
Two fields matter. schema_name is the theme's real name, such as Dawn. schema_version is its version number. The name field is only a label the store owner gave their own copy, which is why you sometimes see Copy of Dawn or Production Theme.
Try it now: Shopify Theme and App Detector →
What the Theme Store number means
If the block has a theme_store_id, the theme was installed from the official Shopify Theme Store. Updates for those themes can be applied from the store's admin.
If it says null, the theme is not from the Theme Store. It may be a premium theme bought from another marketplace or the theme maker's own site, a custom build by an agency, or a heavily modified copy. Updates then have to be applied by hand.
When the theme looks like something else
Custom builds often carry the agency's or brand's own name, so no known theme comes up. That is normal for larger stores. A custom theme can still be built on top of a well known one, and the page source usually will not tell you.
A store that runs a headless build, where the storefront is separate from Shopify's own, will not publish these details at all.
Can you use the same theme
If it is a Theme Store theme, yes: you can add it from the Theme Store, and many are free. A premium theme is bought from the person who made it. A custom build cannot be copied, and you should not try.
Even with the same theme, two stores look different. The theme is a starting point. Layout choices, photography, copy and apps are what you actually see.
What to do with the answer
For your own store, the version tells you whether you are behind on updates. For a competitor, treat the theme as a clue and not a recipe. Stores convert because of clear offers and fast pages, and the theme alone explains very little of that.
If you are choosing a theme, compare how fast the live demo loads on a phone, not just how it looks.