They're similar illnesses caused by different viruses.
Both cause fever, coughing, body aches, fatigue, and sometimes vomitting and diarrhea. Both can be mild, severe, and even fatal. And both can result in pneumonia. Similarly, both can be spread person to person, through droplets in the air from coughing, sneezing, talking, spitting, all of that shite. And both can spread by an infected person days before symptoms appear (maybe weeks in terms of COVID-19 - we don't really know yet).
I think the biggest differences between flu viruses and coronaviruses (because COVID-19 is just 1 coronavirus, other coronaviruses include SARS & MERS) is it's a different family of diseases. And as far as we know, COVID-19 - our "novel 2019 coronavirus" is caused by the strain of virus going around. With the flu we know it's caused by several different types and strains of the influenza virus.
The other biggest difference is the higher mortality rate we're seeing from this coronavirus than we see from most strains of the flu. And of course, that because it's a new virus we don't have people who are immune to it & there's no vaccine currently.