Everything is the difference, the only thing they have in common is the needle that penetrates the skin ? You're asking a question that has as many answers as there are tattooers. I would advice you to go premium and read all the threads on the topic, it has been asked and answered over and over and over Welcome to the forum! ??
Very simplified version,
coils are driven by magnets and more volt is more power/punch... Rotaries are driven by a motor where more volts is more speed.
Also related, cartridges work well with rotaries but suck on coils. Coils can be fully tweaked and rebuild, can't really do that with rotaries.
Neither is better per se, it's largly down to personal preference I'd say.
But like MalligaMallan mentioned, plenty of information and heated debates on this topic in the premium section
One pushes the needle in to the skin, the other pulls the needle in to the skin, which works better ? What ever gets the job done to deposit the ink in to the skin with minimum trauma, what works for one may not necessarily work for another ?
Try both to get your own perspective , I started with coils and I like them , but right now I use rotary. I will probably like to use both for different techniques in the future , but right now I focus on rotary , there is tons of rotary vs coils information on YouTube.
If your planning to buy a cheap chinese machine I suggest a rotary it's easier to make good copys at rotary than coils, since the construction and function is easier to understand in a rotary, most coil knock off really sucks at least the once I tried , you need to be patient and learn tuning and changing machine parts of your planning to use a coil, coil maschines is a whole world of knowledge , and it is very interesting . But in a minimalistic perspective I would say rotary are more convenient , less things to worry about , less parts needed etc .
I hope you can try both to find out what you prefer.