Varnish -- Issues

I'm new here, so I apologize if this post is in the wrong area.

Story: I spilled a bottle of nail polish remover on a wooden table. It didn't removed the finish, just the varnish. I ran and bought a sanding sponge thing and a semi-gloss and a satin varnish. I sanded the area and applied the satin first -- it wasn't shiny enough. I sanded it again and applied the semi-gloss. It matches, but now there are obvious edges to it.
Obviously, I have no idea what I'm doing. It's sort of an urgent issue -- this is my cousin's table.

Can anyone help?

If you are having trouble matching, take it all off and start again. You shouldn't need to sand, just use fine steel wool as you remove the old finish.