I was a military policeman and investigator for 25 years.
Crime scene examination/investigation is the use of specialised techniques (e.g. fingerprint recovery, DNA recovery) while searching and examining a scene, in order to find, preserve and record evidence in relation to an alleged crime.
The route to a career in crime scene examination varies, depending on the jurisdiction, but you can often get into it via a career in law enforcement. In other words, once you have gained sufficient experience as a police (peace) officer (civilian or military), you can apply to attend a crime scene examiner's course, on successful completion of which, you will be employed (supervised and eventually solo) on such duties.
While I am not a crime scene examiner, I have worked with them a lot. The main attributes for the job are, as you might expect: patience, attention to detail, a methodical approach, excellent record keeping, flexibility (You will find yourself on duty/on call during weekends, public holidays and nights) and excellent verbal and written communication (You will be required to produce written reports and to give evidence in writing and sometimes verbally in court).
A forensic scientist has more of a lab-based role, usually examining or analysing exhibits recovered by a police officer or crime scene examiner. The path to a forensic science career is a good science degree, followed by specialist education and training, followed by employment in a crime lab.