Conceptually they are they same (just flipping GPIO bits), but practically you can do things with one which you can't do with the other.
There is no operating system on an Arduino, like there is on a Pi. This means you can do much more "real-time" things on an Arduino, like bit-bang a serial port. This is hard to do on a platform with an OS, because the OS process scheduler might pull your program off of the CPU for a few milliseconds. If you need to do something to those pins 1,000 times per second or more, you're out of luck.
If you've ever seen a large scrolling LED marquee sign which appeared to have an occasional "stutter" in the scrolling, that's most likely because it was being controlled by an operating system.
The difference between the two has to do with resources, architecture, and peripherals. Arduino is a low power, low cost, low memory, low speed 8-16bit microcontroller. A raspberry pi is a complete 64 bit computing system with 1-2GB of RAM and the peripherals you'd expect on most desktops. Arduino use Atmega chips while Pis use ARM cores. You need to program in a language supported by gcc for Arduino, but RPis can use the LLVM infrastructure.
https://www.raspberrypi.org/forums/viewtopic.php?f=72&t=7226...
And I think I was totally mistaken on RTOS's, I could have sworn there was a port of FreeRTOS for the RPi but it looks like that isn't really floating around.
[1] https://gitlab.denx.de/Xenomai/xenomai/wikis/Supported_Hardw...
For resources the Arduino.cc forum and tutorials are a great place to start. Should be able to find some project ideas as well.
So I have raspberry pis; I have arduinos. I've done some simple programming for both, to read from sensors. Water sensors and thermal sensors and buttons and sound pins all on breadboards were fun.
I figured I was ready for the next step: soldering together a kit. So I soldered together an ethernet kit for the arduino. That project fell flat: the arduino powered up while the ethernet shield did not; the arduino reported that it didn't even "find" the ethernet controller even though it was piggy-backed onto it. Usually when you plug in the RJ45 jack to a NIC you at least get the lights on the RJ45 port to light up. But no dice for me here either. And I have no idea how to debug that problem.
After that, turn on power and verify that each trace has the correct voltage on it.
The two steps above should let you determine which part is failing.