Serverless Computing / Headless Commerce

Both are synonyms for using the cloud instead of a own server. Cloud means most a 3rd party system and therefore its some kind of pay per use model.
You could use Amazons S3 for data storage or you could use spryker or commercetools if you need for example a basket and a checkout system for something you want so sell but you dont want to implement your own shop.
Your app is then the frontend and it communicates eg via JSON to the cloud.

Nothing new, just new Marketing-Words