What is the core difference between Microsoft Office 2019 and Microsoft Office 2021?

For version details, have a look at https://docs.microsoft.com/en-us/officeupdates/update-history-office-2021 (older perpetual licenses can be selected from the navigation pane on the left).

It is worth noticing that the main version number is 16 (the same for Office 2016, 2019, and 2021).

See What's new in Office 2021

I'm biased, but I'd say the most significant improvement is the introduction of dynamic arrays in Excel, accompanied by several new functions.

There is no "core" difference between Office 2019 and 2021, for 2 reasons.

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First, there is no "office" application. Office is a marketing scheme to sell various bundles of applications. The bundle of apps is the same in 2019 and 2021.

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Second, the changes to the individual applications are peripheral. All of the features / functions in 2019 are there in 2021. (Yes, for the nit pickers, sometimes MS deprecates or removes a VERY few features, but effectively none.) Each of the 2021 apps have a few more features than 2019.

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As Hans pointed out, Excel is the application that tends to get most of the neat new features.

This is MS's page that lists most (not all!) of the new features in the various applications

https://support.microsoft.com/en-us/office/what-s-new-in-microsoft-365-95c8d81d-08ba-42c1-914f-bca4603e1426 

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If you tell us which applications you use most, then we can chime in with the new features we liked most.

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The new features are a SUBSET of the new features added to 365 since the last new release, ie 2019. They are definitely not all of the new features.