Ethereum Sharding vs Polkadot Parachains

First of all I am learning, so I might be (most probably) wrong comparing these two things.

Ok, yesterday I saw twit saying that Polkadot now ready for Parachain launch. Quick read on Parachain reminded me about Ethereum's shard chains, where you have one Beacon chain and all other 64 (63) chains will join it. Don't you think this is very similar approach to scalability? Will or is there any plans Ethereum could join Polkadot as a parachain? All ideas are welcome.