Electrum 3.0 is out and the addresses are starting with bc1 apparently. I have a hardware wallet in the other hand where SegWit is supported too but the addresses are starting with 3 instead. What are the differences and are they compatible between each other (including the old addresses). Could I receive/send without having to worry?
Of course they are compatible. The original developers of Bitcoin created segwit. But you should not confuse it with segwit2x which is a disgrace.