In standard usage, bi- means two and semi- means half (a bicycle has two wheels, a semicircle is half a circle). Thus biweekly and bimonthly both mean every two of their respective interval, and semiweekly and semimonthly mean twice during their interval.
This simple distinction becomes muddled by the standard use of biannual to mean every half year rather than every two years (see biannual, biennial, or semiannual). To avoid confusion, 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 in casual settings.