I use the term "lone parent", although my situation is different from what you've described.
Nowadays, "lone parent" seems more fitting since my partner lives with us and does contribute to a) household bills b) buys the kids things if he sees them aka trainers/ clothes/takeaways etc. c) light discipline aka "[child name] put your shoes away before your mum trips over them"
DP doesnt contribute with the daily grind of morning wakeup calls, lunches, dinners, football training etc (he works away Mon-Fri), he doesn't get involved in the top level discipline or the foundations I built long before I knew he existed. So, he doesn't get to claim "parent" status, in my book. However, I cant claim "single mother" status because I do have help which is appreciated and I know he would be there to help the kids with anything they needed at the drop of a hat.
What I consider myself, in both these scenarios, had zero to do with the biological fathers involvement. He did not factor in the way I ran my life when he did see them (he's out of their life now, hurrah!), but previously his visitation was never close to 50/50.