I don’t have a dedicated camera. Just using an iPad, not good enough though. Distant shots are grainy, and fast-paced mages get blurred.
You have arrived at what you think is a solution to your problem (high pixel count, long distance shooting) and have asked about that. Instead, I'd encourage you to take your solution, shelve it, and instead ask the meta-questions: What resolution is necessary to take shots of some type (portraits, wildlife, etc), what focal lengths are needed for some type of shot (city, landscape, etc), and what types of cameras are available to meet my (now much more defined) needs?
You need to better understand your problem before trying to make a solution.
Distant shots are grainy
This is because the iPad/iPhone doesn't actually "zoom" to take shots. It has a fixed wide angle lens. When you tell it to zoom-in, what you're actually doing is telling it to crop the image and interpolate the result up to the normal resolution. Obviously, you can't create pixels out of thin air. Interpolation algorithms have become pretty darned good, but they have their breaking point where the image falls apart, appearing grainy/pixelated/unsharp/etc.
I'd actually encourage you to not bother zooming in at all. Simply take the shot and crop later - it's the same thing.
Your frame of reference for distance is also informed by your use of the iPad. It has a very wide angle lens - the type most use to capture a very large scene. So when you say that you need to capture something far away, you need to define that - as in, do you need to see someone's head and shoulders who is standing 20 yards away? Or do you need to see the whiskers on a cat that is 100 yards away?
The first of these examples is not that "zoomed-in" at all for the photographic world while the second is much, much more "zoomed-in." The first is much cheaper to obtain, while the second is out of reach for most people's budget.
fast-paced mages get blurred
Your iPad is akin to using a dedicated camera on full auto mode. While it can use really fast shutter speeds, it doesn't inherently know to do this. The limit with your iPad is the fact that the aperture is fixed. Normally, a camera can adjust exposure using aperture, shutter speed, and ISO but in the case of your iPad and its fixed aperture, you have only the ISO and shutter speed to play with.
Lower ISO's product less noisy, cleaner, sharper looking images. So, it's no wonder that your iPad is favoring the lowest ISO (thus slowest shutter speeds) for an exposure. Most people take selfies and shoot non-moving objects, so erring on this side means more good images for more people. Obviously, it's not true for fast moving objects.
You will see an immediate jump in your ability to shoot moving objects by downloading a camera application that lets you directly set the ISO and shutter speed so that you can force a faster shutter speed when you need it.
At some point, you will hit a wall and no longer get faster shots - this is where your ISO is maxed at its highest setting. The only solution here is to add light to the scene, if possible. You'll also suffer some image quality degradation at high ISOs, and if you want better high ISO performance, you will need a larger camera sensor (don't worry, every dedicated camera uses a sensor larger than the one in your phone).
About your solutions...
Resolution is less important than you think. Any dedicated camera made in the last 5 years will have plenty enough for you, unless your plan is to print images greater than 12"x18".
As above, focal length at great distance really, really needs to be nailed down. If it turns out that you need <200mm lenses...these are fairly cheap. If you need greater than that, well...they're not cheap at all. The best budget telephoto in the Canon line-up is the 400mm f/5.6, and its ~$1,000 all by itself.
Options that you have available to you are:
- Clip on lenses like these. Some are junk, some are good. They won't fix your shutter speed problem but they can "get you closer" to the action optically.
- Point and Shoot cameras. You'll get some zoom optically but the image quality will still be on par with your phone, if slightly better.
- Bridge cameras. Bigger zooms are available and the image quality will be a tad better.
- Mirrorless Interchangeable lens cameras and DSLR's. Best image quality and most versatility/flexibility in this list. Also the most expensive.
Before you make any hard decisions about what you need, I'd encourage you to better understand what is causing you problems, exactly the type of image you want to make, and then reach out to places like this for advice on solutions available. You don't know what you don't know, so ask.