blockchains can solve many things. but first to find a solution you need the "why"

yes blockchains are blocks of data, but WHY need 10,000+ random people to store 3D print files?
yes blockchains are blocks of data, but WHY need to think of a blockchain as just a payment token method when theres already thousands of chains that are payment tokens

a solution could simply be that 20 torrent servers or file hosts store the files. and a blockchain just stores a description of the file and a filehash
that way the blockchain is used as proof of authenticity. to even get on the blockchain users have to verify a file has no viruses and the file is as described to pass the test to get confirmed.
then the 10,000+ random users are only storing
"1000th scale design Eiffel tower: filehash:xxxxxxxxxxxxxxxxxxxxx"
instead of mb's of data of the file itself.
so that when searching the internet or getting emailed/sent a file/torrented. the file can be instantly verified to be what it suppose to be and be a clean copy

there is no need to use blockchains as the actual datastore of files, especially if blockchain users dont need to store the whole file for the rest of their life. blockchains could just be the modern day replacement of the 'patent office'

If the case is the transmission of raw files to be printed by the 3D printer, I guess it mainly focuses on the commercial aspect of the 3d Printing company as it really doesn't increase the functionality of the printer but will enable it to print peer to peer and could accommodate transactions over large queue of requests.

But if we think of the fact that 3D printing as of today is now a serious thing as it prints important tangible things, incorporating blockchain for the security of the files to be printed would be a great help.

Quite a lot.  They are both areas worth lots of money but both are of no practical use to most people.

What do they have in common - nothing.
However, as in many industries, blockchain tech can be used to verify the source/owner of something. In this case say you make a 3D model of a specific widget and charge for the STL file to it. Blockchain could be used to verify who created the file, owns the rights to it and that the file is unchanged from when it was entered into the blockchain tracking system.

Yes a private database is able to do the same thing but usually does not allow the Public to query it. A distributed (Public) Ledger does let the 3rd parties query it. The only remaining question would be who runs the chain.