Determining the relative popularity of various licenses is actually quite difficult. Below are two graphs.
The first is taken from BlackDuck: Top 20 Open Source Licenses:
and list the following top 5 (making up 76 % av the total):
- GPLv2 (24 %)
- MIT/Expat (20 %)
- Apache 2.0 (16 %)
- GPLv3 (10 %)
- modified BSD (6 %)
The second one is taken from presentation at the 2013 Linux Foundation Collaboration Summit Licensing of Software on Github: A Quantitative Analysis:
and list the following top 5 (making up 82 % av the total):
- MIT/Expat (36 %)
- modified BSD (13 %)
- GPLv2 (13 %)
- GPLv3 (12 %)
- Apache 2.0 (8 %)
There is a lot of interesting data in the Linux Foundation Collaboration Summit presentation (e.g. the distribution between permissive, copyleft, weak copyleft and dual licensing, and the shift over time towards more permissive licenses). I recommend clicking through all the slides.
While the source and methodology of these studies differ (and only the presentation made at the Linux Foundation Collaboration Summit explains the methodology used), both list the same licenses as the top five, but their relative position differ.
While these stats are not definitive (and I hope other answers can show us more studies of this type), I think it is quite likely that these licenses are among the most used ones.
As for how "they differ in their most important terms and conditions?", that would make a very long answer. However, the FSF has a very good page about various licenses and comments about them, here are direct links to each of the top 5, with a note stating whether the license is copyleft or permissive - as this by far is the main difference between the FLOSS licenses.
- MIT/Expat - permissive
- modified BSD - permissive
- GPLv2 - copyleft
- GPLv3 - copyleft
- Apache 2.0 - copyleft, but allows downstream relicensing to GPLv3