Car Q: Are an "engine coil" and an "ignition coil" the same thing?

Please say yes!

Yes.

Yes!
(Of course I don’t know that to be true. But since you asked…)

The only point worth adding is that on some cars built in the last 15 or so years, a single coil which works in conjunction with a distributor style device has been replaced with direct ignition where each cylinder is fed by it’s own coil. Google “direct ignition system” if you’d care to read more.