Recently I saw a great page called Amazon Web Services in Plain English. I searched for the Azure equivalent, and as it turns out, one doesn't exist! Time to set that straight.

The most interesting thing about this exercise is that Azure services are actually named fairly well. For each of the official names, it was extremely difficult to come up with a better name.

Base Services

Azure Service Could be Called Use this to... Like AWS...
Virtual MachinesServersMove existing apps to the cloud without changing them. You manage the entire computer.EC2
Cloud ServicesManaged Virtual MachinesRun applications on virtual machines that you don't have to manage, but can partially manage. 
BatchAzure Distributed ProcessingWork on a large chunk of data by divvying it up between a whole bunch of machines. 
RemoteAppRemote Desktop for AppsExpose non-web apps to users. For example, run Excel on your iPad.AppStream
Web AppsWeb Site HostRun websites (.NET, Node.js, etc.) without managing anything extra. Scale automatically and easily.Elastic Beanstalk
Mobile AppsMobile App AcceleratorQuickly get an app backend up and running. 
Logic AppsVisio for Doing StuffChain steps together to get stuff done. 
API AppsAPI HostHost your API's without any of the management overhead. 
API ManagementAPI ProxyExpose an API and off-load things like billing, authentication, and caching.API Gateway

Mobile

Azure Service Could be Called Use this to... Like AWS...
Notification HubsNotification BlasterSend notifications to all of your users, or groups of users based on things like zip code. All platforms.SNS
Mobile EngagementMobile PsychicTrack what users are doing in your app, and customize experience based on this data. 

Storage

Azure Service Could be Called Use this to... Like AWS...
SQL DatabaseAzure SQLUse the power of a SQL Server cluster without having to manage it.RDS
Document DBAzure NoSQLUse an unstructured JSON database without having to manage it.Dynamo DB
Redis CacheEasy CacheCache files in memory in a scalable way.Elasticache
Storage BlobsCloud File SystemStore files, virtual disks, and build other storage services on top of.S3
Azure SearchIndex & SearchAdd search capabilities to your website, or index data stored somewhere else.CloudSearch
SQL Data WarehouseStructured Report DatabaseStore all of your company's data in a structured format for reporting.RedShift
Azure Data LakeUnstructured Report DatabaseStore all of your company's data in any format for reporting. 
HDInsightHosted HadoopDo Hadoopy things with massive amounts of data. 
Machine LearningSkynetTrain AI to predict the future using existing data. Examples include credit card fraud detection and Netflix movie recommendations. 
Stream AnalyticsReal-time data queryLook for patterns in data as it arrives. 
Data FactoryAzure ETLOrchestrate extract, transform, and load data processes.Data Pipeline
Event HubsIoT IngestorIngest data at ANY scale inexpensively. 

Networking

Azure Service Could be Called Use this to... Like AWS...
Virtual NetworkPrivate NetworkPut machines on the same, private network so that they talk to each other directly and privately. Expose services to the internet as needed. 
ExpressRouteFiber to AzureConnect privately over an insanely fast pipe to an Azure datacenter. Make your local network part of your Azure network.Direct Connect
Load BalancerLoad BalancerSplit load between multiple services, and handle failures. 
Traffic ManagerDatacenter Load BalancerSplit load between multiple datacenters, and handle datacenter outages. 
DNSDNS ProviderRun a DNS server so that your domain names map to the correct IP addresses.Route53
VPN GatewayVirtual Fiber to AzureConnect privately to an Azure datacenter. Make your local network part of your Azure network. 
Application GatewayWeb Site ProxyProxy all of your HTTP traffic. Host your SSL certs. Load balance with sticky sessions. 
CDNCDNMake your sites faster and more scalable by putting your static files on servers around the world close to your end users.Cloudfront
Media ServicesVideo ProcessorTranscode video and distribute and manage it on the scale of the Olympics.Elastic Transcoder

Management

Azure Service Could be Called Use this to... Like AWS...
Azure Resource ManagerDeclarative ConfigurationDefine your entire Azure architecture as a repeatable JSON file and deploy all at once.CloudFormation

Developer

Azure Service Could be Called Use this to... Like AWS...
Application InsightsApp AnalyticsView detailed information about how your apps (web, mobile, etc.) are used.Mobile Analytics
Service FabricCloud App FrameworkBuild a cloud optimized application that can scale and handle failures inexpensively.