Hey Rose,
1)
For Ajax Search results, I m searching with this SKU – 5202240101000002, please see the Screenshot SS-1-hp.png
For Usual search button results, i m searching with this 5202240101000002, Please the Screenshot SS-2-hp.png
2)
For Search with Product Name, i m searching with this name – ENJOY غرفة نوم , and you can see in the Screenshot SS-3-hp.png that other products also come in search results along with the term i searched.