Unable to create a loop to compare the content of two sheets

a very fast approach is given by the use of arrays and Application.Match() function:

Sub GetPartialMatch()
    Dim paramlist1 As Variant, paramlist2 As Variant
    Dim cel As Range
    Dim i As Long

    paramlist1 = Sheets(1).Range("A2", Sheets(1).Cells(Rows.Count, 1).End(xlUp)).Value ' collect all sheets(1) column A values in an array
    paramlist2 = Sheets(2).Range("A2", Sheets(2).Cells(Rows.Count, 1).End(xlUp)).Value ' collect all sheets(2) column A values in an array

    For i = 1 To UBound(paramlist1) ' loop through paramlist1 array row index
        If Not IsError(Application.Match(paramlist1(i, 1), paramlist2, 1)) Then Debug.Print paramlist1(i, 1) ' if partial match between current paramlist1 value and any paramlist2 value, then print it
    Next
End Sub

if you want an exact match just use 0 as the last parameter in Match() function, i.e.:

If Not IsError(Application.Match(paramlist1(i, 1), paramlist2, 0)) Then Debug.Print paramlist1(i, 1) ' if exact match between current paramlist1 value and any paramlist2 value, then print it

BTW, if you need an exact match you could also use Autofilter() method of Range object with xlFilterValues as its Operator parameter:

Sub GetPartialMatch2()
    Dim paramlist As Variant
    Dim cel As Range

    paramlist = Application.Transpose(Sheets(1).Range("A2", Sheets(1).Cells(Rows.Count, 1).End(xlUp)).Value) ' collect all sheets(1) column A values in an array

    With Sheets(2).Range("A1", Sheets(2).Cells(Rows.Count, 1).End(xlUp)) ' reference sheets(2) column A cells from row 1 (header) down to last not empty one
        .AutoFilter field:=1, Criteria1:=paramlist, Operator:=xlFilterValues ' filter referenced range with 'paramlist'
        If Application.WorksheetFunction.Subtotal(103, .Cells) > 1 Then ' if any filtered cell other then header
            For Each cel In .Offset(1).Resize(.Rows.Count - 1).SpecialCells(xlCellTypeVisible) ' loop through all sheets(2) filtered cells but the header
                Debug.Print cel.Value2
            Next
        End If
        .Parent.AutoFilterMode = False 'remove filter
    End With
End Sub

You want a double loop.

Sub GetPartialMatch()
    Dim paramlist As Range
    Dim cel as Range, cel2 as Range ; declare all variables!

    Set paramlist = Sheets(1).Range("A2:A" & Cells(Rows.Count, 1).End(xlUp).Row)

    For Each cel In Sheets(2).Range("A2:A" & Cells(Rows.Count, 1).End(xlUp).Row)
        For Each cel2 in paramlist 'Sheets(1).Range("A2:A" & Cells(Rows.Count, 1).End(xlUp).Row)
            If InStr(1, cel(1, 1), cel2, 1) > 0 Then  
                Debug.Print cel(1, 1)
            End If
        Next cel2
    Next cel
End Sub

Always use Option Explicit. Always.

This may be easier using a helper column and a formula, where the row in the helper column indicates TRUE if a MATCH is found. No VBA then. And it will be inherently faster.

Have you tried adding in:

Application.Screenupdating = false
Application.Calculation = xlCalculationManual

...Code...

Application.Screenupdating = true
Application.Calculation = xlCalculationAutomatic

These turn off the screen updating and automatic calculation of formulas within your instance of excel which can help speed up code a lot, you just have to remember to turn them back on at the end or you might give yourself a bit of a headache. It should be noted, though, that if you turn off screenupdating you won't be able to see the results roll in. You'll have to scroll backwards at the end

Another thing to consider would be store the data in an array before hand and doing the operations to the array and simply pasting it back in to the sheet. Accessing the sheet excessively slows down code drastically. Working with the accepted answer provided by @AJD, I made a few changes that will hopefully speed it up.

Sub macro()

Dim paramlist() As Variant
Dim DataTable() As Variant
Dim cell1 As Variant
Dim cell2 As Variant

paramlist() = Sheets(1).Range("A2:A" & Worksheets(1).Cells(Rows.Count, 1).End(xlUp).Row).Value
DataTable() = Sheets(2).Range("A2:A" & Worksheets(2).Cells(Rows.Count, 1).End(xlUp).Row).Value


For Each cell1 In paramlist
    For Each cell2 In DataTable
        If InStr(1, cell2, cell1, 1) > 0 Then
            Debug.Print cell1
            exit for
        End If
    Next cell2
Next cell1

End Sub

I would have suggested this under the accepted answer as a suggestion, but unfortunately, I don't have enough rep to comment yet.

Edit: switching the order of the for loops allows you to insert a more efficient exit for and can allow you to skip large portions of data within the search array

Not sure if this is any faster (it uses pretty much the same algorithm, a loop inside of a loop), but I would argue it's a bit clearer:

Sub SearchForPartialMatches()
    Dim needle1 As Range, needle2 As Range

    Set needle1 = Excel.Worksheets(1).Range("$B$2")

    Do While needle1.Value <> ""
        Set needle2 = Excel.Worksheets(2).Range("$B$2")

        Do While needle2.Value <> ""
            If InStr(1, needle1.Value, needle2.Value) > 0 Then
                Debug.Print needle1.Value, needle2.Value
            End If
            Set needle2 = needle2.Offset(rowoffset:=1)
        Loop
        Set needle1 = needle1.Offset(rowoffset:=1)
    Loop

End Sub

The main difference is it's not looping over the entire column, but instead starts at the top, and uses the offset method until there are no more rows (with data).

Of course, you'll need to change the starting cell for needle1 and needle2.

I ran this with the EFF large word list copied into both sheets, and it ran in about 4 minutes (which was less time than with @AJD, but that might've been a fluke). YMMV.

Just one more option. Not much different from any suggestions above ... The concept is to speed up processing by minimizing VBA - Excel interactions by loading the values to arrays and processing arrays like this:

Dim cel as String, cel2 as String
Dim arr1() as String, arr2 As String

arr1 = Sheets(1).Range("A2:A" & Cells(Rows.Count, 1).End(xlUp).Row)
arr2 = Sheets(2).Range("A2:A" & Cells(Rows.Count, 1).End(xlUp).Row)

For Each cel In arr1
    For Each cel2 in arr2
        If InStr(1, cel, cel2, 1) > 0 Then  
            Debug.Print cel
        End If
    Next cel2
Next cel

I'd like to know if it helps at all :)