On the surface the terms seem to be identical translations: theosis (θέωσις, Greek), deification (Latin). However, as Normal Russel’s book carefully shows, theosis was only first used in 363 with Gregory of Nazianzus. However, the cognate term theopoieo (θεοποιἐω) was used as early as Clement of Alexandria (c.150-c.215) and Hippolytus of Rome (d.235). Theosis was not used regularly until byzantine times, with Ps. Dionysius and Maximus the Confessor laying the foundation for its popularity.
On the other hand, deification was not as popular in the Latin church (Russell only mentions Tertullian, Hilary of Poitiers, and Augustine), so there was not a comparable evolution of terminology surrounding the theology as with the Greek writers. Divinization is also a Latin term that carries a similar significance but has not been used as often. As to the distinction between divinization and deification, it seems there is a former debate over divinization (theosis) by Energy [good] vs. deification (apotheosis) by Essence [bad]. However, many use deification (e.g., Andrew Louth) and understand it as deification by energy.
Conclusion: 1) As we speak about the development of the doctrine it best to use ‘deification’ as a more generic term. Specifically, it does not employ an anachronistic, byzantine term–theosis–for the early development of the doctrine in the Greek fathers. This is exactly how Russell treats the terminology in his analysis of the Greek tradition. 2) However, if we are speaking of the concept from a systematic theological point of view, it seems to me that theosis or deification would be virtually equivalent (like, for example, kavod [Heb.] and doxa [Gk.]).
I recently had a very helpful email exchange with Carl Mosser, who also promoted conclusion #1 but not #2. He made a distinction between ‘deification’ as the proper Christian view of salvation and ‘theosis’ which is a later (inappropriate) mystical turn influenced by philosophical thought (e.g., Ps. Dionysius and Maximus). I would lean more towards a thesis recently promoted by Donald Fairbairn in the recent version of JETS on “Patristic Soteriology: Three Trajectories?”, where the mystical has roots much earlier in Clement and Origen and so is not technically a ‘later’ turn. I, however, have many more primary sources to read to develop my own informed opinion.