Short Answer : No.
Long Answer :
adb install is a "shortcut" that is equivalent to open a shell (using
adb shell) and type
pmstand for package-manager and his behaviour is the same as other package manager in other Linux distributions (like
aptitude in Debian or
pacmanin Arch Linux) except that
pm doesn't fetch package from a distant location.
The Play Store is an application like others, and we can't call android applications like we call a program like a C or "normal" Java program, because the
.apk file isn't actually a binary, but a simply zipped package. It is the Dalvik Virtual Machine (sort of equivalent to the Java VM) that deals with running applications. The Play Store application simply download the application you want and then run
pm install on the package downloaded.