What is difference between current flowing through metals and current flowing through liquid?

Metal conduct electricity with the help of free electrons whereas in liquids, ions are mainly responsible for the conduction of electricity. 
Please note not all the liquids conduct electricity, only liquid which have ions or are contaminated with ions are capable of conducting electricity. 
Some liquid which have free electrons also conducts electricity for example mercury.
Kindly refer to the following links:
https://www.meritnation.com/ask-answer/question/does-conduction-of-electricity-in-liquids-occurs-through-ele/chemical-effects-of-electric-current/6980632
https://www.meritnation.com/ask-answer/question/why-do-metals-conduct-electricity-and-non-metals-dont/electrolysis/858211

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