New rules for this category went gone into effect starting with the 2013 Hugo Awards.
The Constitution of the World Science Fiction Society currently defines a Semiprozine as follows:
3.3.12: Best Semiprozine. Any generally available non-professional periodical publication devoted to science fiction or fantasy, or related subjects which by the close of the previous calendar year has published four (4) or more issues (or the equivalent in other media), at least one (1) of which appeared in the previous calendar year, which does not qualify as a fancast, and which in the previous calendar year met at least one (1) of the following criteria:
(1) paid its contributors and/or staff in other than copies of the publication,
(2) was generally available only for paid purchase
Professional is defined as such:
3.2.11: A Professional Publication is one which meets at least one of the following two criteria:
(1) it provided at least a quarter the income of any one person or,
(2) was owned or published by any entity which provided at least a quarter the income of any of its staff and/or owner.