Another issue that the Lightning Network has to deal with is that users should actually stay online to check the open channels, because otherwise a malicious counterparty will be able to close the channel based on an outdated ‘intermediate’. In principle, the Lightning Network penalty mechanism will then take effect, but then your lightning node must be online to detect the fraud.
Watchtowers are a way to outsource that control to a third party, so you don’t have to keep your lightning node online all the time.
Partially Signed Bitcoin Transactions (PBST) are, as the name implies, bitcoin transactions that are partially signed. This is useful, for example, for transactions that require multiple parties to sign. Now the well-known MultiSig or MuSig is often used for this, but they have the disadvantage that the transaction has to be built up in one go before it can be sent to the network. So everyone has to sign first before the transaction is offered to the network.
With a PSBT that is not necessary and it is possible to send a partially signed bitcoin transaction to the network. Other parties involved can then view and verify the PSBT at a later time and, if they agree, also sign with their private keys.
Electrum was originally released in 2011 by Thomas Voegtlin (but later helped by others) and it was one of themthe first ‘light wallets’ that made bitcoin accessible to a wider audience. With a light wallet, or SPV wallet, you don’t have to run your own node or download the complete blockchain, which made bitcoin a lot more user-friendly for many people. Today, most bitcoin wallets are light wallets.
However, keep in mind that if you use a light wallet, there is a bit more trust involved than if you run your own bitcoin node as with the Bitcoin Core wallet. You use light wallets (unless you set otherwise) to connect to a bitcoin node of another. Cryptography still protects your bitcoins against theft, but you have to trust that the bitcoin node you connect to provides you with the correct information about the blockchain. This can be important during a hard fork or an attack on the network. Also, the privacy of light wallets is a bit more vulnerable, because the bitcoin node you connect to may be able to see which transactions come from you.
For many people, these are acceptable risks in most cases, but for the highest level of security, running your own bitcoin node is essential.