Different companies, but offering competing services.

If you have an app, you can host with AWS, Azure, Digital Ocean or Heroku or Google App Engine.

They offer different tools, setup, supported frameworks, configuration options, and pricing also.

Although Heroku is hosted on top of AWS, but AWS, Azure, Digital Ocean, and Google all have their own datacenters (or rent datacenters).

There are comparison tables out there, but generally there is usually a trade off for easiness of setup, how much dev ops skills you have vs. flexibility and price (some price scheme works out better if you are small some price scheme works out better if you are big).

Is Digital Ocean a wrapper on AWS/Azure? It seems like DO offers plain VMs that you can use for whatever you need. In that respect it seems more similar to AWS and Azure than Heroku. It provides you the infrastructure to run your apps. The way you deploy and manage them is up to you.

Heroku in my experience abstracts things further so that you don't spin up your own VM. Instead you use Heroku's UI and tools to install applications and use Heroku's resources. Heroku attempts to help developers focus on apps instead of infrastructure.

From what I understand you could build something like Heroku on Digital Ocean.

I may be mistaken though. I'm not an expert in Digital Ocean so I am not sure if they offer a platform-like experience similar to Heroku.