Can I make Terminal.app open different profiles with shortcut like iTerm?

Create a window just how you like it, then under the "Shell" menu of Terminal.app select "Export Settings...". Save the file with a file name, and the resulting file can be used to open a new terminal window with the same settings.

Save a Terminal.app profile as described in Peter Murray's answer and then set up a shortcut for it using Better Touch Tool. BTT is primarily intended for adding touch pad gestures but you can also assign keyboard shortcuts. Create a shortcut to open your saved profile ("Open Application/File/Script...") and you'll get a new Terminal.app window running that profile.