Taking it from the top. Blazor is a framework used to build interactive web applications with HTML, CSS and C#. It also allows developers to build rich web applications with Razor Components that use the Razor syntax and C# code for your application. 

Blazor provides the flexibility to host those components on a server (with Blazor Server) or on a client machine (with Blazor WebAssembly). 

Blazor WebAssembly

• components in the browser using a WebAssembly based .NET Runtime
• Handles UI updates on the client-side completely
• Uses open web standard for WebAssembly to run the code - no plugins or transpilation required
• Can use programming language of choice on server
• Best for high fidelity, instant update applications like games or drawing apps
• Requires modern browsers (of which all support WebAssembly) to run
• Still in preview and under active development

Blazor Server

• components in the browser using a WebAssembly based .NET Runtime
• Hosts UI components on the server
• Allows you to take full advantage of .NET Core on the server
• Uses SignalR to push UI updates for specific components
• Has the full performance and security that comes with .NET Core
• Can continue to use familiar ASP.NET Core technologies on the server, side by side
• Works best when you know the client can maintain a connection to the server
• Ideal for use on low powered client devices, since components do most of their work on the server
• Generally available with the release of .NET Core 3.0