What user documentation or other tool help resources do you have with you to find this answer. Can you list the help and user documentation you have please, so we know where to refer you? (There is no mention of the tool you are using)
This is really a context question, but from what I have seen with http load testing, the Failed Transactions is usually an environmental issue (network time out, server not available etc.) while the error is an application issue. The error is usually 'trapped' via some sort of 'text check'.
Without more context, however, it is difficult to answer this.
Failed transaction is a situation when TCP or lower connection (IP, physical...) breaks in the middle. Error, however, is ususally a response sent by server, notifying about missing page, bad authentication etc. If you're in windows - use perfmon to monitor failed transactions