Two Datasets Same Query
if (this.ValueTextBox.Text.Length &gt; 0)
{
    value = Convert.ToInt32(this.ValueTextBox.Text);
}


This will throw a nullpointerexception if Text is null, use TryParse instead

int value;
bool result = Int32.TryParse(ValueTextBox.Text, out value);
if(result){
 // use value
}


I don't recommend you using SelectedIndex, because it breaks your code if the ordering get changed in the future, I would use SelectedItem instead.

Notice that you are repeating code, which is not a brilliant idea.

TheTypeForThis gr01 = null;
TheTypeForThis adapter = null;
switch (this.ServerComboBox.SelectedIndex)
{
    case 0:
        gr01 = new GR01.TargetVDNDataTable();
        adapter = new ICMQuery.Models.GR01TableAdapters.TargetVDNTableAdapter();
        break;
    case 1:
        var ds01 = new DS01.TargetVDNDataTable();
        var adapterNew = new ICMQuery.Models.DS01TableAdapters.TargetVDNTableAdapter();
       break;
}

 if (value == 0)      
 {
    adapter.Fill(gr01);
 }
 else
 {
    adapter.FillByPeripheralNumber(gr01, value);
 }
 this.FindScriptsDataGrid.DataSource = gr01;