Microsoft Azure ExpressRoute is a private connection to the Microsoft Enterprise Edges for ExpressRoute (AS 12076). Microsoft than peers within the Microsoft global network with the Microsoft Services. so the way is dedicated connection for expressroute from provider -> expressroute edge -> azure service
Microsoft Azure Peering Service is purely using the Internet connections. A provider can directly route traffic to the microsoft global network on the shortest path without using expressroute. That allows cheap and very performant interconnection to microsoft services and to other providers. No dedicated connection is needed and can be done via any internet media incl. Mobil, DSL, FTTH etc.

If the provider leverages a private network interconnect with Microsoft Internet Peering AS8075 it is like using an ExpressRoute Microsoft Peering but much much cheaper, nearly some performance and you get end to end telemetry data. Think of it like premium internet which is no longer a black box for you.

Cheers,
Flo

As long as the services are free, you can keep it but you cannot use paid services.