Both APIs and CSVs provide us our transaction history. There is less chance of data tampering when uploading through an API, and we suggest you use APIs when possible. However, in some cases, like Bittrex, we may need both API and CSV.
"CSV" stand for "comma separated values" and is another term for an Excel spreadsheet. This will be a file you get from your exchange or wallet, and then upload to ZenLedger.
"API" stands for "application program interface." It allows two software tools or systems to communicate with each other. You will not need to download anything from your exchange or wallet, as ZenLedger will communicate directly with it for the data. 

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