Emergency fund is money kept for personal or family needs
No, you are wrong here, emergency funds is the money kept aside that stands as the last layer of protection of your Bitcoin holdings, it's the money kept aside to use in sorting out any real life emergencies that may threatens your holdings.
and back fund is money kept for future in any personal or business sector.
while back up fund's is that spare money kept aside with the purpose of backing up your investment, like using it to invest aggressively during a dip or you can use it to for some other stuff that may have warrant you to dip into your emergency funds, but take note that your emergency funds is the last layer of protection of your Bitcoin investment, that's why it's very unwise to use it for anything else, except a real life emergency situation that threatens your bitcoin holdings.
Emergency funds, reserve funds and float are all back up funds. This is because emergency funds is the backup to your bitcoin investment and should be tampered with last after you have spent your float and reserve funds incase you lose your job. Reserve funds acts as a back up funds to your emergency funds and that's why you don't touch your emergency funds until a real life emergency plays out. Float is the backup to your reserve funds.