In a traditional database [...]
Ok, let's take a look at the similarities between a traditional database and a public blockchain.
- both store structured data
- both can be updated through transactions
- both can be queried to request data
To query data from a traditional database, you just connect to it and send your request. Notably, the database provider, in this case, can be compared to a full node of a public blockchain because the database software tracks each update to the database and provides you with the results. The main difference is, that the traditional database does not store historical states and also in most cases does not store the transaction history.
I don't want to download the whole blockchain, but I want a "snapshot" of data for a particular smart contract. What is the easiest way of doing so?
Technically, this is not possible. To get a snapshot of a certain state, you will have to know all historic states and commit all transactions to compute the subsequent states until you get to your snapshot block. So the short answer to your question is: run a full node.
However, there are obviously services that allow you to access the latest state, such as https://archivenode.io. This does not really answer your question, but it should help you to get an understanding of why you cannot simply export data without running a node.