An Arduino is a development board, not really intended for an OS (but people have tried it). It allows GPIO control and sensing via GPIO’s, general purpose inputs and outputs. You read a one or zero from a pin. Or you set a value of one or zero on an output pin. This is under software control. Hence, my Arduino Mega 2560 has just a USB device port and a supply connector. Nothing more. It is basic but used everywhere in development, like in IoT.
A Raspberry runs an OS, there are quite a few ported already. It has ethernet, USB host, HDMI out, micro USB, an SD card slot and GPIO’s. It is a complete computer, connect a keyboard mouse and monitor, use an SD card with raspbian or another OS and you boot a computer, not so powerful as the intel and AMD desktops, but still. Several use cases are possible, a media center, streaming video, or surf the web, as VPN server, NAS or edit documents. They have a different use.
Interesting as well: How can raspberry pi be useful?
Raspberry pi website.