Open list
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Open list describes any variant of party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected. This is as opposed to closed list, in which party lists are in a pre-determined, fixed order by the time of the election and gives the general voter no influence at all on the position of the candidates placed on the party list.
Finnish parliamentary election uses the open list method. Here an official poster rack in central Helsinki displays the candidates and their assigned ballot numbers by party.
Ballot during the Finnish parliamentary election of 2011
A campaign bus in Tokyo for (successful) Communist proportional candidate Tomoko Tamura in Japan's 2016 Councillors election. Tamura received roughly half of her votes in Tokyo, other proportional candidates on the same list won most of their votes in other prefectures. The proportional district is nationwide; but limited by a very short legal campaign period, some proportional candidates focus their campaign efforts on only certain regions where they personally or their party have a local base.
Party-list proportional representation
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Party-list proportional representation (list-PR) is a subset of proportional representation electoral systems in which multiple candidates are elected through their position on an electoral list. They can also be used as part of mixed-member electoral systems.
Poster for the European Parliament election 2004 in Italy, showing party lists