There are different types of searches for sales, purchases or mortgages. The searches differ also depending on whether property is registered land, or unregistered land and whether it is leasehold or freehold - you may be searching for different things.
When selling:
Perhaps a Registry of deeds search and/or planning search to guard against something unforeseen showing up later.
When buying:
Registry of Deeds or Land Registry, planning on the proeprty, Judgement, Bankruptcy searches against the vendor - is there anything to impede them selling? e.g. bankruptcy or judgment mortgages
When mortgaging:
Similar but searching against the mortgagor - you.
So if you were buying a property and then mortgaging, your own solicitor would be searching against the property, the vendor and you.
Does this explain it to you?
mf