A private key – is a randomly generated integer number from a certain range. From which a corresponding public key is derived. The private key can not be derived from a public one. It must be kept in secret because it is used to prove an ownership of the corresponding public key, or, more precisely — the address, derived from it.
A public key – is a number that is derived from the private key by an elliptic curve cryptography. Public keys are the basis for bitcoin network addresses.
An address – is a unique identifier in the bitcoin network (or other cryptocurrency network). It is derived from the public key and is used for routing transactions i.e. receiving and sending coins.
Legacy address — is a standart for bitcoin network address that was suggested by Satoshi Nakamoto. It is also called P2PKH (Pay To Public Key Hash), because it requires a public key and a signature computed from a private key from the receiver. This addresses start with a number 1, use mixed case lettering and can be 25-34 characters in length.
P2SH(Pay To Script Hash) address was defined in BIP-0016. As the name implies, using P2SH a receiver must provide a script matching a script hash and data that evaluates script to true. Script, in turn, in simple terms, is a list of conditions for gaining access to the funds on it. These conditions may include, for example, the presence of 2 out of 3 signatures. This way with the advent of P2SH address it became possible to create multi-signature addresses. Structurally P2SH addresses do not differ from the Legacy ones – they consist of the same character set and have the same range of length. But they can be distinguished by the first character – they start with a number 3. These addresses also can be called Compatibility or sometimes SegWit addresses, because they are compatible with SegWit technology, though they were introduced before it and are not it's native solution.
Bech32 – is a bitcoin address that is fully compatible with SegWit.
It was suggested by BIP-0173. It can also be referred to as SegWit address, Native SegWit address or P2WPKH(Pay to Witness Public Key Hash).
Those addresses are case insensitive and start with bc1.
Transactions that utilize SegWit are cheaper and significantly faster than traditional bitcoin transactions, and transactions that utilize native SegWit(i.e. Bech32) addresses are faster and cheaper than others.
A transaction — is a transferring of bitcoin from address to address that is broadcast to the network and collected into blocks. Transaction consists of inputs and outputs. Inputs of the transactions generally are the outputs of the previous transactions.
An unspent — is a single unused output of the transaction.
In the bitcoin blockchain received input must be spent completely, but may be spent to several recipient addresses. A change - is a part of the amount spent, which is returned to your own address. Change is being unconfirmed until the transaction itself is unconfirmed.
Bitcoin network – is a blockchain that is kept alive by such actors as miners. It is their job to append new blocks to the existing chain in a cryptographically secure way. The network provides for the possibility of the reward for their work for each transaction. There is no minimal amount required to pay. But after broadcasting to the network your transaction gets to the common pool of transactions from which miners collect them in order to form a block. So by increasing the fee you can motivate miners to grab your transaction faster. And by setting the fee too low you risk getting stuck with a pending transaction for hours or even to never get a confirmation. In order to prevent such issues some wallets perform an analysis of the transaction pool and offer you the optimal values.
Fee bumping – is an increasing of the transaction fee while it is unconfirmed in order to make it get to the block faster.
RBF – is a fee bumping method, which utilizes bitcoin blockchain’s concept of replacing unconfirmed transaction with another one. So when the transaction gets stuck due to the small network fee it is possible to replace it with the same one with a higher fee. To do so the initial transaction must be marked with RBF flag.
CPFP – is a fee bumping method which utilizes bitcoin blockchain’s opportunity to spend unconfirmed unspents. A new transaction that spends the output of the unconfirmed transaction is created. It is called a child transaction, whereas initial transaction is appropriately called a parent. To confirm a child transaction miner has to add to the block a parent transaction also. So by spending child transaction with a high fee, it is possible to motivate miner to confirm your initial transaction faster.
SegWit — Segregated Witness — is an implemented protocol upgrade intended to provide protection from transaction malleability and increase block capacity. SegWit separates the witness(signatures and scripts) from the list of inputs.
BIP - Bitcoin Improvement Proposal - is an open-design document for introducing features or information to Bitcoin.