Difference between documents with 'docx' and 'dotx' filename extensions

I know that .docx is a Microsoft Word document format and .dotx is a Microsoft Word template format. But what's the difference for the end user?

From my own experience I can say that opening a .dotx file in Microsoft Word has the same effect as copying .docx document and working on a copy in the application.

Am I missing the purpose of templates? What are the advantages of using them over copying and pasting pre-laid out .docx file?

If you open a .dot (or .dotx), there is no ‘save’, it is always interpreted as ‘Save as’.
The main effect of this is that users cannot accidentially save their filled version over the template, which otherwise is quite annoying for the next template user.

You are correct that otherwise there is little difference; after all, you can make a doc or docx to a template by simply renaming the file on disk.

Am I missing the purpouse of templates? What are the adventages of using them over copying and pasting pre-layouted .docx?

Opening template may be faster and "copying" process is on Word, not on user.

For example if you would like to programmatically create new Word files, instead of copying existing file (where you need to input location before you even begin working on document itself) or creating new file and applying formatting, you "open" template and after you're done you can decide on saving or discarding new file (instead of deleting existing copy).

It is understandable that for some use, these advantages are not appealing.

.dotx files are designed to be saved to a specific location on your computer, which will tell word that there is a template available each time you open a new document. You can have as many templates as you want, which comes in handy if you have multiple clients, or multiple reports that need to follow established formatting. ("save as," *.dotx to: this PC > Documents > custom office templates folder)

When you open a new document in Word, just under the search bar, are two tabs, 1) Featured (showing all of the templates available online) and 2) Personal. Clicking personal will show all of the templates that are installed on your computer. It pulls up a blank document that is pre-formatted and you proceed as normal. You never have to hunt for the original, or worry about overwriting previous work.