Hi,
Cross Sectors: Every Antenna is connected with 2 cables called feeders. If the feeders of 1 sector is interchanged with the other sector then this is called a sector swap or cross sectors. It means that the sectors will behave differently, for example 1st sector and 2nd sectors cables are swapped then 1st Sector will behave as a 2nd Sector and vice versa.
Examples:
1. Totally cross sector
in this case S1 is totally changed with S2

2. DCS cross sector
In this case DCS is changed between two sectors (S1,S2)

Cross Feeder: In this type of swap we observe that a single cable (out of 2) in 1 antenna gets swapped with the single cable of another antenna. This can again happen within the same sector or between sectors.
Examples:
1. GSM Cross feeder

2. DCS cross feeder

You can find more examples in the following links:
https://betelecomengineer.blogspot.com/2013/12/explain-2g-problems-faced-telecom.html?m=1
http://ftp.actix.com/resources/1502/Projects/KB/TechLayer/Crossed_feeder_Analysis.htm
Hope it helps!