Hey Sk Zaid,

EEE: In EEE, students have to studyElectrical as well as Electronics. It is the study and application of electrical systems for use in different environments and contains basic electronic courses and more power system.

ECE: Here, aspirants deal with Electronics with some part of communication. The subject uses the scientific knowledge of the behaviour and effects of electrons to develop devices, systems, or equipment that uses electricity as part of its driving force. Also it contains basics on electrical machines and more on integrated circuits and communication systems.

All the best!

electrical engineering students deal with all the electrical stuff like

Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism. This field first became an identifiable occupation in the later half of the 19th century after commercialization of the electric telegraph, the telephone, and electric power distribution and use. Subsequently, broadcasting and recording media made electronics part of daily life. The invention of the transistor, and later the integrated circuit, brought down the cost of electronics to the point they can be used in almost any household object.

where now electric and electrnic engineering deals with electric stuff but also they study electronic stuff mainly Voltage in DC so

Electrical and electrical engg and most preferable then only electrical engg

Electrical engineering (EE) and electrical and electronics engineering (EEE) are two popular specialization of engineering.  both seem very similar,  but Both the branches have a difference. In EEE, few core subject of Electronics are merged with Electrical Engineering course. EEE students have knowledge of digital and analog electronics, microprocessors, embedded systems, communication and in signal processing with electrical engineering  knowledge.
EE students may learn about electrical machines, power systems, controls and instrumentation, power electronics and power systems operation and control. EEE students may learn basic electronics subjects like semiconductor devices, solid state physics, linear electronics, embedded systems, digital electronics, advanced electronics and maybe a subject related to integrated circuits as well.

Some companies specifically request electrical engineers, but most will take in electrical and electronics engineering graduates as well. Some exams like the Engineering Services Examination (ESE) only have an option of electrical engineering, and not electrical and electronics engineering. Today, both these streams need to go hand in hand because of future technology.

Job prospect will differ a lot from college to college for both the branches.

Good Luck