These are two different things.
Coding with AI assistance is what a software developer does who is using AI to a greater or lesser extent to help in their work. The end result is expected to be code that the developer understands (whether they wrote it themselves or not) and that meet the project's standards for code quality and such.
Vibe coding is someone using AI to build a relatively simple application that they would not have either the capability or the time to build on their own, generally to meet a specific use-case or "scratch an itch" that would otherwise go unscratched. In this case, the developer may or may not have any relevant software development skills, and does not need to understand or even read the generated code. If something doesn't work as expected, they give the AI further instructions to hopefully solve it. The end result does not meet any particular coding standards, and is likely not good quality maintainable code, but in many cases it gets the job done.
As a tool to enable non-developers to self-serve a solution for some relatively simple use-cases, i see vibe coding as somewhat analogous to excel or other applications that allow non-developers to build stuff that solves their problem, without writing code themselves. The excel formulas and automations that lurk in the giant spreadsheets that are passed around non-tech workplaces might make a software engineer scream in horror, but most of the time they get the job done.