They are not the same as a PCN. Parking Charge Notice that typically get issued by Traffic Wardens.
Private parking firms are essentially just invoicing for breach of contract and are non-enforceable unless they pursue the case in the civil court, this can very costly and time consuming, for most part their letters demanding payment are just bluster.*
*
Note this is in no way considered legal advice and shouldn't be used as such -Ignoring a Parking Charge is at your own risk. 