I am currently researching ICE's - Integrative and Conjugative
Elements, using a review called Conjugative transposons: the tip of
the iceberg, by Vincent Burrus, et al, and published in Molecular
Microbiology (2002), 46: 601-610. What I specifically need to know is
what distinguishes these elements from typical plasmids, transposons
and other mobile elements etc, as the paper is very confusing.

I'm not going to look at the paper, but I can clarify a few things.

Plasmids can be transmitted by bacterial conjugation, but they are by
definition extra-chromosomal elements, and do not integrate into the
recipient's genome.
Transposons do integrate into the host genome, but are not transmitted
between bacteria by conjugation

The elements these people are talking about do both, and that's what
makes them interesting. In animals you see a continuum from
retroviruses, to those that lost the ability to replicate outside the
cell and have become transposons. I guess this shows that an similar
thing occurs in bacteria with plasmids.