Plasma chains are child chains, not side chains.
"The easiest way to distinguish [a] Plasma Childchain from a Sidechain is the security aspect. OMG Network's Plasma Childchain is anchored to Ethereum and its security is based on Ethereum smart contracts... A Sidechain is attached to Ethereum using a peg that enables one- or two-way transfer of assets ... and relies on its own security mechanisms." - source
"Plasma child chains and sidechains are not the same, in that a sidechain relies on its own validation process to determine the security of that chain, whereas a Plasma child chain may have its own validation process too (such as a PoS layer) but its security ultimately depends on the validation of its root chain (Ethereum). A very big difference, pointed out in the Plasma whitepaper" - source
"Plasma isn't a sidechain! Final security comes from the root chain, but the Plasma chain itself also has security properties that do not rely on trust of the root chain. Whereas sidechains (such as Blockstream's Liquid, or Loom's Dappchains) by definition must trust the main chain. The underlying design principles are different." - source
For more information about the Plasma framework, check out learnplasma.org
For an easy to understand version of the Plasma whitepaper, check out this ELI5
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