You comments are essentially accurate, however, I'd characterize the difference as Republicans wanting to nominate justices who are faithful to the constitution and faithful to their role as arbiters of legal disputes and not a quasi legislative branch, while Democrats want justices who will interpret, sometimes fancifully, the constitution in their modern, ideological view of what society should be.
It seems, lately at least, that Democrats don't want "originalist" justices because they don't like the constitution, as written. They favour justices who take the written text and interpret it in their own progressive speak. It's why Republicans are often disappointed in the performance of their nominees, latest example being the Chief Justice, because their nominees frequently side with the Democrat nominees in creative interpretation. I can't think of a single Democrat nominee who has disappointed liberals in their performance - they are robotically faithful to liberal ideology, regardless of the content of the constitution.