In short: A stablecoin is a crypto token that promises a stable value against a currency (for example €1) or against assets; how stable it is depends on what backs it and who holds the backing.
Simply put: Some are backed by money, some by other assets, and some are "algorithmic" — no reserve, just a formula. In the EU, MiCA distinguishes e-money tokens (issued only by banks and e-money institutions; holders can redeem them at par at any time and free of charge) from asset-referenced tokens (with a separate reserve protected if the issuer fails). Paying interest to holders is banned for both.
Example: You hold 500 tokens "1 token = €1". With an e-money token under MiCA you can ask the issuer for €500. An "algorithmic" stablecoin gives no such right — TerraUSD lost its link to the dollar in May 2022.
Watch out: "Backed by an algorithm" is not backed. Ask what backs it, who holds it and what happens if the issuer fails.
Source: Regulation (EU) 2023/1114 (MiCA), arts. 36, 40, 48–50 — https://eur-lex.europa.eu/eli/reg/2023/1114/oj