A stablecoin constitutes a protocol-based, chain-native token which has a stable price relative to an arbitrary value (i.e., USD $1) and aims to track the return of the sovereign currency on a public blockchain. In the cryptocurrency realm, peg refers to a given price the token aims to stay at. While there is no generally accepted taxonomy for stablecoins, we prefer to use a risk-based approach and distinguish between two basic categories: stablecoins which require trust in a third party (custodial stablecoins) and stablecoins which replace the trust required with economic mechanisms implemented through smart contracts (non-custodial stablecoins).[1]
Basic building blocks of a stablecoin design. Every stablecoin design uses one or a combination of multiple blocks.
Note: A centralized and a collateralized stablecoin (or a decentralized and a non-custodial stablecoin, respectively) are not the same thing. ­­­While these terms often are used interchangeably, they actually characterize two different properties of the stablecoin: Centralization describes the governance layer of a stablecoin, while (non-)custody is an asset layer property. There can be centralized non-custodial stablecoins designs and vice versa.
Note 2: Further, off-chain and custodial collateral are note the same thing. While these terms are often conflated, off-chain and on-chain simply describe the technological mechanics of the collateral. On-chain collateral can be custodial or non-custodial, but not vice versa. Custodial stablecoins are, inter alia, subject to counterparty and censorship risks. "Off-chaining" exacerbates these risks. This is important to understand, as decentralized non-custodial (and therefore strictly on-chain) stablecoins are one of the best and arguably the trillion dollar use case for crypto.
[1] Similar: Klages-Mundt, A., Harz, D., Gudgeon, L., Liu, J. Y., & Minca, A. (2020, October). Stablecoins 2.0: Economic foundations and risk-based models. In Proceedings of the 2nd ACM Conference on Advances in Financial Technologies (pp. 59-79).