Carson G. did a solid job on his answer, and I have a bit to add. The two overlap enough that the confusion makes sense, and the structural similarity you noticed is real. Both build a claim, support it with reasons and evidence, and address the other side. The difference sits in the goal and in how each one treats evidence and the reader.
A persuasive essay aims to move the reader toward a position or an action. The writer starts from a conclusion and works to bring the audience to it, so the essay can lean on emotional appeal, value language, and rhetorical force alongside evidence. Success is measured by whether the reader is convinced. That goal gives the writer some license to select the evidence that helps the case and to frame it in the most compelling way.
An argumentative essay aims to establish a claim as reasonable through evidence and logic. The writer still takes a position, but the work is built to hold up under scrutiny, so it weighs evidence more even-handedly, represents opposing views fairly, and lets the reasoning carry the weight rather than the appeal. Success is measured by whether the case is sound, not only by whether the reader ends up agreeing. The argumentative mode treats the reader as someone evaluating the reasoning rather than someone to be won over (Lunsford and Ruszkiewicz, Everything's an Argument).
A short way to hold the two apart is to ask what each one does with the opposing view. Persuasive writing tends to raise the other side in order to knock it down. Argumentative writing tends to engage the other side seriously, since the strength of the claim depends on surviving the strongest objections to it.
In practice the line blurs, and most strong academic writing leans argumentative because instructors want to see reasoning that holds up rather than rhetoric that pushes. Much classroom writing labeled persuasive in earlier grades becomes argumentative in college work, where the standard shifts from convincing the reader to demonstrating that the claim is well founded.
Source:
Lunsford, Andrea A., and John J. Ruszkiewicz. Everything's an Argument. Boston: Bedford/St. Martin's.
Inactive Tutor
well, you nailed it really. what else can I add?!:)01/19/21