What is the difference between E/Z isomerism and cis/trans isomerism?

is a subset of E/Z isomerism.

cis/trans nomenclature is effective only when the alkene has two different groups on each carbon atom of the double bond and each carbon has one of the same group.

The structure with the pink groups on opposite sides is trans. The structure with the pink groups on the same side is cis.

Structure II below has the two chlorine atoms locked on opposite sides of the double bond. This is the trans isomer.

(from commons.wikimedia.org)

The cis isomer (Structure I) has the two chlorine atoms locked on the same side of the double bond.

There are problems when compounds get more complicated. For example, could you name these two isomers using cis and trans?

Many chemists would follow the longest chain through the double bond. Others might make a different choice.

To remove the ambiguity, we use the E/Z system.

You can always use the E/Z system. It is more reliable and particularly suited to tri- or tetrasubstituted alkenes, especially when the substituents are not alkyl groups.

The cis/trans system is not effective when there are more than two different substituents on a double bond.