You have every right to be confused, the naming has changed a lot and when you wrote the original question the Blazor team had recently renamed 'Server Side Blazor' as 'Razor Components'. That has thankfully since been abandoned, see the timeline below for more on that.
To anyone finding that the naming conventions in the answers here don't seem to marry up with what they are reading in older blog posts it's worth knowing that the meaning of 'Razor Components' has changed repeatedly over time.
This may also help anyone like me who has been using Blazor since near the beginning and feels sure that the names have changed!
TL; DR
The naming has evolved a lot during the pre-release period. Kudos to the Microsoft and the Blazor team for trying to come up with clear names and being willing to change back when needed. However, this has left a legacy of mixed naming conventions in older articles and some Blazor veterans sometimes use older naming conventions.
At the time of writing in September 2020, with Blazor at version 3.2, the official naming convention is:
The exciting history of Blazor naming
October 2018: 'Razor Components' becomes the new name for 'Blazor Server Side'
When Blazor 0.6.0 was released it was decided to officially name server side Blazor as 'Razor Components'.
Dan Roth discusses that in his Blazor 0.6.0 experimental release now available blog post in October 2018:
We announced last month at .NET Conf that we've decided to move
forward with shipping the Blazor server-side model as part of ASP.NET
Core in .NET Core 3.0. About half of Blazor users have indicated they
would use the Blazor server-side model, and shipping it in .NET Core
3.0 will make it available for production use. As part of integrating the Blazor component model into the ASP.NET Core we've decided to give
it a new name to differentiate it from the ability to run .NET in the
browser: Razor Components.
It's also discussed more in the ASP.NET Core updates in .NET Core 3.0 Preview 2 blog post.
Feb 19: Naming is hard...
Probably due to confusion that was arising, the Razor Components name for Server Side Blazor was expanded to 'ASP.NET Core Razor Components'. This is mentioned in the Blazor 0.8.0 release notes:
Server-side Blazor is now ASP.NET Core Razor Components in .NET Core
3.0 As was recently announced, server-side Blazor is now shipping as ASP.NET Core Razor Components in .NET Core 3.0. We've integrated the
Blazor component model into ASP.NET Core 3.0 and renamed it to Razor
Components. Blazor 0.8.0 is now built on Razor Components and enables
you to host Razor Components in the browser on WebAssembly.
April 2019: Switching back to Server-side Blazor
In April 2019 Blazor server side went into official preview and as part of that the naming for server side Blazor was switched back:
Simplifying the naming and versioning
For a while, we’ve used the terminology Razor Components in some cases, and Blazor in other
cases. This has proven to be confusing, so following a lot of
community feedback, we’ve decided to drop the name ASP.NET Core Razor
Components, and return to the name Server-side Blazor instead.
This emphasizes that Blazor is a single client app model with multiple
hosting models:
- Server-side Blazor runs on the server via SignalR
- Client-side Blazor runs client-side on WebAssembly
… but either way, it’s the same programming model. The same Blazor
components can be hosted in both environments.
Note that in the above description there is no mention of Razor Components at all, now we have two different Blazor hosting models (Client-side and server-side) as ways of delivering Blazor Components to the browser.
Sept 2019 The return of 'Razor Components'
Dan Roth's Blazor and .NET Core release notes for the next few versions no longer mention the term 'Razor Components' at all until .NET Core 3.0 Preview 9 when the term emerges again in the name of the 'Razor component unit test framework prototype'.
May 2020 'Razor Components' = 'Blazor Components'. Introducing 'Blazor Server' and 'Blazor WebAssembly'
By the time we get to May 2020 Razor Components and Blazor Components are now being used as synonyms for each other and the naming for the two hosting models has evolved.
The Blazor WebAssembly 3.2.0 now available blog describes that as follows (my emphasis):
Blazor components can then be hosted in different ways to create your web app. The first supported way is called Blazor Server. In
a Blazor Server app, the components run on the server using .NET Core.
And...
Blazor WebAssembly is now the second supported way to host your Blazor components: client-side in the browser using a WebAssembly-based .NET
runtime.
So.. the term 'Razor Components' is officially dead, right?
It would be so much easier if it was.. it does seem like 'Blazor Component' would be a more natural fit. But no, from the Components section of the official documentation:
Components in Blazor are formally referred to as Razor components.