The bottom number in time signatures has always confused me

It's mostly vibes

The top number in a time signature is easy to understand. Is the song in four? Count "one, two, three, four." Is it in three? Count "one, two, three." Is it in five? Count "one, two, three, four, five." That's all there is to it. However, the bottom number is another story. What is going on down there? I collected various examples of time signatures in this track I made, but I didn't understand why "Solsbury Hill" by Peter Gabriel is in 7/4 but "One More Night" by Can is in 7/8.

I'm not alone in finding this confusing. My students struggle with it too. They are right to! Every explanation I have ever seen of the bottom number is circular. Say we're talking about 4/4 time, so a beat is a quarter note long. Okay, so what is a quarter note? Well, four of them make a measure. And what's a measure? Uh... four quarter notes.