There are subtle differences between an explanatory and a persuasive paragraph. An explanatory paragraph explains an idea, such as this paragraph is doing, while a persuasive paragraph will attempt to convince you of a particular viewpoint.
In a persuasive essay, you pick one side of an argument and argue it with a goal of trying to convince others to agree. In a personal opinion essay, you state your opinion and use evidence/examples to show why it is your opinion, but your goal is not to convince others.
Persuasive writing is trying to convince others that your opinion is correct. Opinion writing is explaining your opinion and why you think that. It uses some to no emotion depending on the topic.
The most common place we see persuasive writing is in advertising. Sometimes it’s the short text of a television advertisement, telling us how much better our lives will be if we buy a particular product. Other times it might be the lengthier ‘advertorials’ – ads disguised as article – in newspapers or magazines.