In Altium, you make the changes in one place (usually the schematic), and then (D)esign->(U)pdate or (D)esign->(I)mport to synchronize between schematic and board.
You can also enable Cross Select Mode (under tools) so that selecting a part in the schematic will select it in the PCB and vice versa. Note that in a multi-channel design you'll need to be in the compiled view, not the editor view (tabs at the bottom of the schematic window) in the schematic for selection to work properly.
For all of this to work properly, you'll need to make sure your component links are accurate, under Project -> Component Links. Copying and pasting or inserting snippets can sometimes break component links, which will break all kinds of things, but it's usually fairly easy to fix.