I have usually understood Enterprise software to mean "software which costs extra, because it is supported by the vendor in a contract". It usually implies "for large organizations" since they can make more money there, but it's still enterprise software even if a single individual buys it.

I think everyone has Enterprise confused with the aircraft carrier. :-)

Enterprise simply means a business, and software for business requires contracts, support, guarantees, and monetary remedies if the software fails due to failures by the vendor.