It is technically possible to distribute apps to iPhones and iPads without going through the App Store.
However, as you indicate that you want to distribute the apps to iPhone/iPads not owned by you or your organization, it narrows the options.
If you want to distribute software to internal test users or external beta testers (or similar), you can use Apple's TestFlight. It allows you to distribute your app to both insider and outsiders without limiting what the app can do compared to an App Store distributed app.
There is however limits to how widely you can distribute apps via TestFlight:
Essentially you can have up to 100 users that are internal (i.e. if you enroll as an organization this would be employees or dedicated extern testers). You can distribute apps to those almost without any delay and without going through a length review process.
You can also distribute your app to up to 10,000 external users. However those apps must go through a (shortened) review, and this means that there is some delay to the distribution. Often you will need to wait 12-24 hours to get the first version of an app approved. Updates are usually quicker.
Finally, TestFlight limits the duration these apps can be used. Essentially when an app is approved for external testing, it expires 90 days later. At that point it will not run on a users device. This means that to ensure people can keep using the app without interruptions, you must release an update 4 times a year approximately.
If you were enrolled in the App Store program as an Enterprise, you also have the option of distributing apps to your users without going through the App Store. Here you can deploy apps directly from MDM, email, web sites, etc. without going through any review process. However, you can only distribute apps to your own employees (i.e. devices owned by the enterprise). You cannot use this method to distribute apps to customers.