IOUs are informal financial instruments that acknowledges a debt between two parties, either in the form of money or physical goods. They are informal as they do not clearly state the repayment date, interests and other key financial terms agreed between parties, that would be specified in a promissory note.
IOUs are a simplistic form of putting a future transaction in writing for later consideration.
It comes handy for transactions between a lender and borrower that already have a financial history and successfully established a trustworthy relationship.
New transactors generally avoid IOUs as they often fall outside of financial regulation and open the door for uncertainty and discrepancies as they are very few legal remedies against it.
An online cryptocurrency wallet is a web service provided by a third party, that allows users to store their private keys online. The keys are not controlled by the wallet owner: it is the service provider that controls them, and therefore owns its underlying assets.
Online cryptocurrency wallet providers act as custodians of digital assets for their customers. In other words, users outsource the storage of their private keys to a third party and trust them to keep them securely.
Storing digital assets on online wallets is the cryptocurrency equivalent of IOUs: the wallet provider promises to deliver the said assets when its customer requests it.
And IOUs are informal. Coupled with the lack of customer protection in the cryptocurrency industry, there is no guarantee online wallet providers will keep their end of the deal. Malicious custodians aren't the only risks: online wallets are vulnerable to hacks and targeted attacks which can wipe out their private keys and therefore, their customer's funds.
Cryptocurrency exchanges have lost billions of funds due to organised hacks. While it'll never be clear if some were inside jobs or genuine external attacks, these exchange customers lost their digital assets and won't see them any time soon.
Storing cryptocurrencies on third party platforms, including exchanges, is unsafe and removes one of the core value proposition of blockchain technology. With cryptocurrencies, users can indeed stay in control of their assets by storing them in either hot or cold wallets.
Avoid online and exchange wallets by all means, those platforms are not safe.