In standard usage, bi- means two (bicycles have two wheels) and semi- means half (a semicircle is half a circle). Thus biweekly and bimonthly both mean every two of their given interval, while semiweekly and semimonthly mean twice during the interval.
This simple distinction is muddled by the standard use of biannual to mean every half year rather than two years (see biannual, biennial, or semiannual), which leads many to confuse the meanings of the other prefixed words. It’s thus safer to prefer writing out the intention in less-rigid writing (especially in corporate settings) than to rely on the prefixes. Both A biweekly meeting and A meeting every two weeks are acceptable, with the latter better-suited to avoid confusion.