In short no. Advertising is marketing but marketing is not advertising.
While they are often used interchangeably, Marketing is an umbrella term that covers advertising as well as social media marketing, search engine optimisation (SEO), branding and often website design.
Advertising is more appropriate when talking about paid activities. These include pay-per-click advertising (Google ads, etc.), out of home (billboards, posters etc.) and TV advertising to name a few.