Tldr: MW’s summary, in order from newest term to oldest:
Jerry-built means “built cheaply and unsubstantially.” Jerry-rigged means “organized or constructed in a crude or improvised manner.” Jury-rigged means “constructed or arranged in a makeshift fashion.”
Side question: why do they call it a “Jerry” can?
Edit: looked it up. It’s a ww2 British slur for Germans
Edit 2: wondered about “Jerry-Rigged” https://www.merriam-webster.com/grammar/jerry-built-vs-jury-rigged-vs-jerry-rigged-usage-history
Tldr: MW’s summary, in order from newest term to oldest: