What is the difference between the M.I.T. and the C.I.D.?

I have worked in the justice sector in the UK, and had never heard of the MIT as a police unit. I presume you believe it stands for Murder Investigation Team - but there is no such unit. The CID investigates all crimes, and in more serious cases an investigation team with the necessary experience wil be formed - including for the investigation of murders. The people in such a team will also do other CID work at other times - especially as in most forces there are not enough murders to keep a team busy full time.

In the Met, they used to have AMITs (Area Major Investigation Teams) which became subsumed into the Homicide and Serious Crime Department in the last reshuffle. Most of them were CID officers but obviously they focussed on major investigations as opposed the normal Divisional work that most CID deal with.

My experience with other forces shows that they all have something similar, basically a pool of CID to deal with serious or complex enquiries.

BTW if a murder occurred in Dublin the Garda would deal with and I have no idea how they operate.

MIT is part of the CID which investigate major crimes my local police force

shares one with the next door county in the UK no idea what they do in Eire

Neither are "departments" therefore they can't have the same goal. M.I.T. stands for Massachusetts Insitute of Technology (a college) and C.I.D. stands for Criminal Investigation Division (a section INSIDE of many police departments).

Massachusetts Institute of Technology and the Criminal Investigation Department.

I see no connection at all!