I thought the point was the ECHR is an international treaty from the early 1950's to which we are a signatory. The problem is that to enforce rights you had to go through a long process with the European Court on Human Rights.
The Human Rights Act 1998 was part of a Labour pledge that they would incoporporate the act into UK law bia statute. The Act contains the ECHR andas pointed out above public bodies cant act in contracention and the courts have to interpet existing statutes in a way that is consistent with the the ECHR. The other difference is that a UK citizen can now approach uK courts for a claim under the ECHR rathern than having to file a compliant in Strasbourg.
So yes they are separate treaty v UK statute, but the latter contains and could not exist without the former. A simple read of the statute makes this clear.