What's the difference between Add-PsSnapIn and Import-Module
Modules came about in PowerShell V2. V2 can still load Snapins though, if necessary. The big difference is that modules can be deployed using Xcopy. There is no need to register anything. To deploy a Snapin, an installer would have to hack the registry, which would require elevated priveleges. To load a module, you simply have to use the Import-Module command.
Modules can have a lot more metadata using a Module Manifest as well, which can specify all kinds of things that might be useful for the end user to know, including version, dependencies on other modules, and which powershell hosts can run the module.
All that being said, if you are writing a binary module in C# or VB, you still use the same PSSnapin base class.
To get more information, check out
PS > help about_modules
In v2, modules are the preferred way organize the cmdlets, providers, functions, aliases, and other commands that you create. You don't install a module. You simply import a module into the PowerShell session using Import-Module cmdlet.
AFAIK, a PowerShell snapin is more of a v1 approach. There are still a few teams at MS creating snapins instead of modules. For example, SharePoint 2010 cmdlets. PowerShell snapins are binaries (.dll) that implement cmdlets and providers. You need to install a snapin and then add the cmdlets in the snapin to a PowerShell session using Add-PSSnapin cmdlet.
This is poorly documented, so take my answer with a grain of salt. Take a look at developer documents for snapin and modules. Briefly, snapin is "just" a .Net assebly whilst module can contain scripts, asseblies and more.