Embedded Linux devices come in many different sizes and varieties. Some may have app stores, but most don't. There are various methods to get the OS and apps on the devices.
Embedded Linux
OS deployment
The deployment of the operating system will on your device, as some embedded devices have very specific methods in which the operating system is deployed to the device. In the case of Raspberry Pi, it is easy to copy the image to an SD card and put that into the RPI and boot it up.
I have a script named writeIso that I use; it consists of two lines:
#!/bin/bash
sudo dd if=$1 of=$2 bs=4M status=progress
I run it something like this:
./writeIso /path/to/deviceImage.img /dev/sdc
Other devices may have a flash method, whereby the image gets copied directly onto the device. This can be as low-level as having to use JTAG, or it could be higher-level, such as using Android's adb command. Sometimes, you have to write the image to an SD card, put that into the device, and then, with some combination of keys or buttons, flash that image into the machine's ROM.
App deployment
With a distribution with a package manager such as Raspbian or Yocto, you can easily distribute your application, either by installing directly on the device or adding to the package repository. In the case of Yocto, you can have a local repository to distribute.
To get the package file onto the device, you can use Qt Creator and set up a generic Linux device. This requires an SSH server running on the device and some kind of network connection.
You can also use the scp command to copy packages and/or binaries to the device. This also requires an SSH server.