The European Convention of Human Rights and the Council of Europe are international in nature. The UK is part of these institutions and organisations through international treaties on the same terms as every other member state. This means that the rules, rights and responsibilities in these organisations and institutions were written collectively by the original countries who founded them.
The Human Rights Act of 1998, on the other hand is domestic law - written in the UK to apply to the UK alone and passed by the UK Parliament. This piece of legislation is what links the UK and its justice system to the ECHR and the European Court of Human Rights.
The Human Rights Act means that UK courts have to interpret UK laws as far as possible so that they are compatible with the ECHR rights, and forbids not just the Westminster Government, but any public authority such as local councils or the Scottish Parliament, from violating any of these rights.