Most titles are registered in Land Registry. There is a folio and LR map.
A small number of titles, especially in the centre of towns or a few rural properties which were never dealt with under the Land Purchase Acts are Registry of Deeds.
So in 99% of cases your title is one or t'other.
There are some cases where title is split between LR and Registry of Deeds - those could be because the title was orginally two different plots, or e.g the leasehold being in the Land Registry and the freehold being registered in the Registry of Deeds.
The PRA now administers both title systems.
The Land Purchase Acts were the legislation whereby the landlords were bought out, and the freehold of tenanted farms vested in the former tenant, the cost being paid off over about 70 years.
IMHO the most important social event in the history of the last two centuries..