you choose one app and you wanna use is on your phone, the fisrt thing you need "download" this app, and the next "install" it, then you can use it.
"download" is the app/software you do not have on your device like your phone or computer, but you want to have it, so you have to download it first. The software installation package is what you download , you can not entre it and use this software through this software installation package.
“install” is when you have the software installation package on your device, you press this package then you will see the "install" is proceed , when the proceed finish you can final use this software/app.
I hope it can helps you.