I want to check for similarity for text in corresponding cells in excel

One way to do this is to use the first column to create a regular expression and apply it against the second column.

One advantage of using regex is that one of the data returned is the start and length of the match -- perfect for addressing the characters property of the range object.

I used early binding (see the reference to be set in the code notes), but you could use late binding if you must.

I also have the data in columns A & B, but you can alter that with the part of the code that defines the data location.

You should NOT need to use any On Error code. Much better to write the code to handle any forseeable errors. I did NOT do any error checking, and that may need to be added.

If speed is an issue, there are various other modifications which can be made.

The constructed regular expression will have the general appearance of

\b(?:nnn|nnn|nnn|nnn)\b

which means to

• match a word boundary
• match any of the pipe delimited substrings
• match another word boundary.

For more information, see How to use Regular Expressions (Regex) in Microsoft Excel both in-cell and loops

Option Explicit
'Set reference to Microsoft VBScript Regular Expressions 5.5
Sub highLight()
    Dim R As Range, C  As Range, WS As Worksheet
    Dim RE As RegExp, MC As MatchCollection, M As Match
    Dim sSplit As String
    
'set the data range
'   one column wide
'   column 2 will be offset 1 to the left
'Obviously you can change this in many ways
'And also work in your user selected method as in your code.
'only requirement is that the ranges be single column, and you can
'easily check for that
Set WS = ThisWorkbook.Worksheets("Sheet4")
With WS
    Set R = Range(.Cells(1, 1), .Cells(.Rows.Count, 1).End(xlUp))
End With

Set RE = New RegExp
Application.ScreenUpdating = False
With RE
    .Global = True
    
    'loop through the first column
        For Each C In R.Rows
            'replace the semicolon with the pipe
            sSplit = Replace(Join(Split(C.Value, ";"), "|"), " ", "")
                
                'since data has a terminal semi-colon, need to remove it if present
                If Right(sSplit, 1) = "|" Then sSplit = Left(sSplit, Len(sSplit) - 1)
            
            'finish construction of the regex pattern
            .Pattern = "\b(?:" & sSplit & ")\b"
            
            'check for matches and change relevant characters font color
            Set MC = .Execute(C.Offset(columnoffset:=1))
            With C.Offset(-0, 1)
                .Font.Color = vbBlack
                For Each M In MC
                    .Characters(M.FirstIndex + 1, M.Length).Font.Color = vbRed
                Next M
            End With
        Next C
End With
End Sub

Similarities

• There is a problem with your data: the values in column A end with an "; ", while the values in column B end with ";". The solution presented is to use only the string before the last semi-colon ; with the Split function.
• To avoid complications, I integrated the code into your rather cool solution.

The Code

Option Explicit

Sub highlightOrig()
    Dim xRg1 As Range
    Dim xRg2 As Range
    Dim xTxt As String
    Dim xCell1 As Range
    Dim xCell2 As Range
    Dim I As Long
    Dim J As Integer
    Dim xLen As Integer
    Dim xDiffs As Boolean
    On Error Resume Next
    If ActiveWindow.RangeSelection.Count > 1 Then
      xTxt = ActiveWindow.RangeSelection.AddressLocal
    Else
      xTxt = ActiveSheet.UsedRange.AddressLocal
    End If
lOne:
    Set xRg1 = Application.InputBox("Range A:", "Similarity finder", xTxt, , , , , 8)
    If xRg1 Is Nothing Then Exit Sub
    If xRg1.Columns.Count > 1 Or xRg1.Areas.Count > 1 Then
        MsgBox "Multiple ranges or columns have been selected ", vbInformation, "Similarity finder"
        GoTo lOne
    End If
lTwo:
    Set xRg2 = Application.InputBox("Range B:", "Similarity finder", "", , , , , 8)
    If xRg2 Is Nothing Then Exit Sub
    If xRg2.Columns.Count > 1 Or xRg2.Areas.Count > 1 Then
        MsgBox "Multiple ranges or columns have been selected ", vbInformation, "Similarity finder"
        GoTo lTwo
    End If
    If xRg1.CountLarge <> xRg2.CountLarge Then
       MsgBox "Two selected ranges must have the same numbers of cells ", vbInformation, "Similarity finder"
       GoTo lTwo
    End If
    xDiffs = (MsgBox("Click Yes to highlight similarities, click No to highlight differences ", vbYesNo + vbQuestion, "Similarity finder") = vbNo)
    Application.ScreenUpdating = False
    
    xRg1.Font.ColorIndex = xlAutomatic
    xRg2.Font.ColorIndex = xlAutomatic
    
    Const Delimiter As String = "; "
    Dim dLen As Long: dLen = Len(Delimiter)
    Dim s() As String
    Dim d() As String
    Dim cString As String
    Dim n As Long
    Dim cStart As Long
    
    If Not xDiffs Then
        For I = 1 To xRg1.Count
            cStart = 1
            Set xCell1 = xRg1.Cells(I)
            Set xCell2 = xRg2.Cells(I)
            cString = Left(xCell1.Value, InStrRev(xCell1.Value, ";") - 1)
            s = Split(cString, Delimiter)
            cString = Left(xCell2.Value, InStrRev(xCell2.Value, ";") - 1)
            d = Split(cString, Delimiter)
            For n = 0 To UBound(d)
                If IsNumeric(Application.Match(d(n), s, 0)) Then
                    xCell2.Characters(cStart, Len(d(n))).Font.Color = vbRed
                End If
                cStart = cStart + Len(d(n)) + dLen
            Next n
        Next I
    Else
        For I = 1 To xRg1.Count
            cStart = 1
            Set xCell1 = xRg1.Cells(I)
            Set xCell2 = xRg2.Cells(I)
            cString = Left(xCell1.Value, InStrRev(xCell1.Value, ";") - 1)
            s = Split(cString, Delimiter)
            cString = Left(xCell2.Value, InStrRev(xCell2.Value, ";") - 1)
            d = Split(cString, Delimiter)
            For n = 0 To UBound(d)
                If IsError(Application.Match(d(n), s, 0)) Then
                    xCell2.Characters(cStart, Len(d(n))).Font.Color = vbRed
                End If
                cStart = cStart + Len(d(n)) + dLen
            Next n
        Next I
    End If
    
    Application.ScreenUpdating = True

End Sub

The heart of your question is how to test for your notion of similarity.

Here is a function which, when given a string consisting of semicolon-delimited items, returns True if the items are the same, though possibly in a different order, and False otherwise. The key idea is to split on ";", sort the resulting array, then rejoin. This will put the strings in a standard sorted order, which can then be directly compared for equality:

Function Sort(A As Variant) As Variant
    Dim sorted As Variant, item As Variant
    Dim lb As Long, ub As Long
    Dim i As Long
    Dim items As Object
    Set items = CreateObject("System.Collections.ArrayList")
    
    lb = LBound(A)
    ub = UBound(A)
    ReDim sorted(lb To ub)
    
    For i = lb To ub
        item = A(i) 'Somewhat oddly, seems needed
        items.Add item
    Next i
    
    items.Sort
    
    For i = lb To ub
        sorted(i) = items(i - lb)
    Next i
    
    Sort = sorted
End Function

Function Similar(s1 As String, s2 As String) As Boolean
    Similar = (Join(Sort(Split(s1, ";")), ";") = Join(Sort(Split(s2, ";")), ";"))
End Function

For example, Similar("12;34;56","34;56;12") will evaluate to True but Similar("12;34;56","34;16;12") will evaluate to False.

In your case you have trailing semicolons so they are not being used as delimiters in a standard way. It turns out not to matter: Similar("12;34;56;","34;56;12;") still works as expected.