What is the difference between the new Minecraft Installer and the older Launcher?

The old launcher used to run Minecraft normally using Java, and Minecraft downloads when you play for the first time. Using the installer, you automatically download Minecraft files and all program files needed to the launcher, which doesn't involve use of Java to run. Minecraft runs in a Mojang custom JVM optimised for Minecraft, which gets installed automatically, so you don't even need to manually install Java to use MC with the new launcher

When the installer is run, the launcher is downloaded to your Program Files directory and a shortcut is created on the Desktop. This defaults to "C:\Program Files" for 32-bit versions of Windows and "C:\Program Files (x86)" for 64-bit versions.

If the shortcut is clicked or double-clicked (depending on your settings), or if the user selects "Run Minecraft" in the installer once it has finished, a program will open and download the Minecraft launcher itself along with a few other components. As soon as it is done, the launcher will open.

Right away, you may notice that the launcher starts up quicker - this is due to bypassing Java on startup. Additionally, all previously created profiles and their configurations will be present. No worries, the structure and location of the game's files hasn't changed, so your profiles and worlds are still usable.

TL;DR: The new launcher no longer requires Java to start, though it is still needed to play Minecraft. Due to its independence from Java, the launcher observably starts up and loads faster.