Firstly, "brown" and "black" don't match anything on sheet 2. They come close to "Brown" and "Black". If you change the uppercase characters to lowercase then this non-elegant solution will work:
Sub test()
Dim arr As Variant, i As Long, j As Long, rw As Long, lr As Long, str As String, newstr As String
arr = Split(Sheet1.TextBox1.Text)
lr = Sheet2.Cells(Sheet2.Rows.Count, 1).End(xlUp).Row
For i = 0 To UBound(arr)
str = Replace(arr(i), " ", "")
For rw = 1 To lr
If str = Sheet2.Cells(rw, 1) Then
newstr = newstr & Sheet2.Cells(rw, 2) & " "
j = 1
End If
Next
If j = 0 Then newstr = newstr & str & " "
j = 0
Next
Sheet1.TextBox1.Text = Left(newstr, (Len(newstr) - 1))
End Sub
If you think you'll have the first word of the sentence (eg Black is the new grey) then add "Black" and "Grey" onto Sheet2.