AppleScript: get filename and extension

filename-of-posix-path.scpt

-- Description
-- Get filename or extension of POSIX path

set p to "/Applications/Safari.app"
set pFile to POSIX file p

tell application "Finder" to set theFullFileName to name of file pFile
-- Get filename "Safari.app" with extension

tell application "Finder" to set theFileExtension to name extension of file pFile
-- Get extension "app"

set xtsLength to count of theFileExtension
-- Get extension "app" length: 3

set theFileName to text 1 thru -(xtsLength + 2) of theFileName
-- Get filename "Safari" without extension

filename-of-selected-file.scpt

-- Description:
-- Get filepath, filename and extension of selected file

tell application "Finder" to set theFilePath to POSIX path of (selection as alias)
-- "/Applications/Safari.app"

tell application "Finder" to set theFullFileName to name of (selection as alias)
-- "Safari.app"

tell application "Finder" to set theFileExtension to name extension of (selection as alias)
-- "app"