There are various channels in which you can distribute your app. Google and Apple makes up the lion's share of apps that are submitted so they will be discussed the most.
The Google Play Store is the easiest app store to deploy to for Android devices. Apps are scanned for malware and now has a human review process like Apple iOS apps to ensure an app does not do adverse things to an Android device. However, its content is not filter. There is also a faster turn around time when the app is submit and when it appears in the app store, typically within a few hours.
An Android app is confined to a sandbox which means that only certain areas (e.g., storage) can be accessed by means of permissions that the developer registers. A new feature call Verify Apps compares an app to a large database of known malware. If there is a match, a user is given a warning and has the opportunity to cancel the installation.
There is ONE legitimate iOS app store and that is the Apple App Store. And unlike Android which is highly fragmented in regard to devices and OS's, there are only a few iOS devices (e.g., iPad, iPhone, iPod) that uses basically the same OS.
The Amazon App Store is primarily designed to serve apps for Kindle Fire devices. To search for an app, select Apps and Games from the search drop down menu and then type an app name and click the Enter key. However, other users can get an app through the Amazon Appstore by downloading it.
Besides the three stores mentioned above, there are other app stores you can use to submit your apps:
There are many other stores which focused on particular regions (e.g., Asia and Africa). However, submitting to them all manually can be a time consuming process. The good new is that there are services the let you submit ONCE and publish in MANY app stores. The website CodeNGo (http://codengo.com) will let you publish one app a year for free to over 30 stores including Amazon, Google Play, Aptoide, etc.