Minting = the creation methode of the token via the original smart contract. Compare a smart contract with a snack machine in which you put in crypto and receive your nft. ​ Buying = mostly you buy a NFT via Opensea or some other NFT marketplaces. This is the secondary market. In this case you just transfer the ownership from person x to person y. ​ Hope this helps! :-)

Minting is a form of buying first hand from the creator (primary market)> ​ Buying is a more general term, where one can buy anytime from anyone from the secondary market.

I count minting like going to the store and paying for the item yourself, normally thats how you will get the best price too. When saying buying an nft I imagine getting it via secondary.

Another difference between minting and buying, yet not mentioned in the answers, is what you get. ​

• When you buy an NFT you tipically choose what you buy, depending on what you like more, on the floor price, or the rarity. You look at what is available on the secondary market and you choose the one to buy. ​
• On the opposite, when you mint an NFT you don't know the output, since you are the person that is triggering the birth of the NFT. You might obtain something super rare, something common, something that you like a lo or something that you like less.