A deacon receives the Sacrament of Holy Orders and is ordained, and is therefore a clergyman.
If a deacon is married at the time of ordination, he remains married; but does not remarry if his wife passes away: a widowed deacon must remain unmarried. Also if he is unmarried at the time of ordination, he must remain unmarried (celibate.)
Formerly,the Catholic Church had "Major Orders" (bishop, priest and deacon/subdeacon) and "Minor Orders" (acolyte, exorcist, lector and porter/usher.)
In 1972, the minor orders were renamed "ministries" and are now carried out by laypeople, both men and women: now it's just lector, acolyte and usher.
Exorcist is a special, rarer role with extensive specialized training. I don't think all dioceses have an official exorcist, but Pope Francis is encouraging the expansion of the Order of Exorcists. I believe an exorcist is always a priest.
Traditionalist Catholics who use the 1962 Roman Missal still observe the traditional Major Orders (considered clergy) and Minor Orders (considered laity). I'm thinking maybe Eastern Rite Catholics do too (??)
That's the basic outline, but I may be a little fuzzy on the details. It's shifted a bit over the last century.
The exorcist of any Diocese is always the Bishop. The bishop has the option of delegating that role to a mandated exorcist who is a priest. The distinction is important because authority matters in the preternatural realm. Authority flows from Christ to the Pope to the Bishop to the Exorcist. Any variation in that order is outside the authority of the Catholic Church and subject to demonic exploitation in the case of the possessed.
Some denominations practice deliverance by charism rather than by office and this is biblically justified. However, most often that occurs in cases of affliction rather than true possession. They will sometimes refer to that as exorcism but almost always it is deliverance.