Are the Assembly and Convention the same thing?

No. Essentially, the Convention deals only with delegate selection which will ultimately nominate a candidate for President of the United States. All other party activities are handled by the Assembly. Along each step of the way, when a Convention is required, it is customarily held at the same time and place as the Assembly for the same body. Usually the people who are selected to go to the County, Congressional, and State Assemblies are the same people who are selected to go to the corresponding Conventions. This is not a requirement, just more practical.