Powershell – scripting language. Fileext = .ps1
Tools: Powershell Console and ISE (intellisense capable, tabbed navi, testing scripts etc)
Cmdlets = name for Powershell commands (Get-Command etc..) installed as part of WMF (WM4 is latest, WM5 is preview). Commands avl may vary by OS, Test-NetConection not avl in Win7, only Win8 and above. Cmdlets and parameters have aliases like dir, cd, cls, del etc.. Params can be partially typed as long as they match up unambiguously.
Modules: PowerShell version 2, modules are packages containing one or more cmdlets which extend the capabilities of PowerShell. Many installed with RSAT (for server mgmt) and can be downloaded and used (use trusted sources and caution). Modules can be used using Import-Module command which makes them avl to current PS session. Advanced users can create Modules for reuse.
Tutorials and Further Help:
Getting Started with PowerShell 3.0 Jump Start
Advanced Tools & Scripting with PowerShell 3.0 Jump Start
Everyday Powershell for Developers