Sikh and Gursikh

What is the difference between these Sikh and Gursikh. Are they same?

Sikh means student or leaner. Gursikh means "student of the guru". When talking about the people that follow Sikhism, we refer to them all as Sikhs, or Gursikhs. In this context they mean the same thing.

Vaaheguru Jee Kaa Khalsaa Vaaheguru Jee Kee Fatehh!

Generally speaking Gursikh and Sikh mean the same thing, but sometimes
It depends on the context in which these words are used.
For example, Guru Sahib says ਰਹਿਤ ਪਿਆਰੀ ਮੁਝ ਕਉ ਸਿਖ ਪਿਆਰਾ ਨਾਹਿ ।
Here Sikh means someone who is liberal in following rehat and does not
meet Gurus standards of GUrmat lifestyle. On the other hand Guru Sahib also says

ਸਤਿਗੁਰੁ ਸਿਖ ਕੀ ਕਰੈ ਪ੍ਰਤਿਪਾਲ ॥

and in the above verses Sikh refers to Gurmukhs who follow GUru teachings.
So there is no clear definition on these terms it often depends on the context
that these terms are used. Us mere mortals can never really define
what it means to be Gursikh; Guru Sahib defines what a Gursikh ( sikh) is in the following
verses.

ਗੁਰ ਸਤਿਗੁਰ ਕਾ ਜੋ ਸਿਖੁ ਅਖਾਏ ਸੁ ਭਲਕੇ ਉਠਿ ਹਰਿ ਨਾਮੁ ਧਿਆਵੈ ॥
ਉਦਮੁ ਕਰੇ ਭਲਕੇ ਪਰਭਾਤੀ ਇਸਨਾਨੁ ਕਰੇ ਅੰਮ੍ਰਿਤ ਸਰਿ ਨਾਵੈ ॥
ਉਪਦੇਸਿ ਗੁਰੂ ਹਰਿ ਹਰਿ ਜਪੁ ਜਾਪੈ ਸਭਿ ਕਿਲਵਿਖ ਪਾਪ ਦੋਖ ਲਹਿ ਜਾਵੈ ॥
ਫਿਰਿ ਚੜੈ ਦਿਵਸੁ ਗੁਰਬਾਣੀ ਗਾਵੈ ਬਹਦਿਆ ਉਠਦਿਆ ਹਰਿ ਨਾਮੁ ਧਿਆਵੈ ॥
ਜੋ ਸਾਸਿ ਗਿਰਾਸਿ ਧਿਆਏ ਮੇਰਾ ਹਰਿ ਹਰਿ ਸੋ ਗੁਰਸਿਖੁ ਗੁਰੂ ਮਨਿ ਭਾਵੈ ॥
ਜਿਸ ਨੋ ਦਇਆਲੁ ਹੋਵੈ ਮੇਰਾ ਸੁਆਮੀ ਤਿਸੁ ਗੁਰਸਿਖ ਗੁਰੂ ਉਪਦੇਸੁ ਸੁਣਾਵੈ ॥
ਜਨੁ ਨਾਨਕੁ ਧੂੜਿ ਮੰਗੈ ਤਿਸੁ ਗੁਰਸਿਖ ਕੀ ਜੋ ਆਪਿ ਜਪੈ ਅਵਰਹ ਨਾਮੁ ਜਪਾਵੈ ॥੨॥

In general we see that people coming to Gurdwara are refered to as sikhs even if they have not accepted Guru Granth sahib as there Guru (I mean they have not taken Khande di pahul). What is the status of people who come to gurdwara to do namaskar to Guruji , sit and listen the katha kiratn, have langar and do some seva? They call themselves sikh, so this question comes to mind Is sikh somebody who is not yet on the right path but might get there someday and Gursikh is one who has taken Khande di pahul and have taken oath that Guru Granth Sahib is there Guru and will follow Gurujis hukum in daily life.
Obviously the gurbani quotes given by Veer Sukhdeep Singh shows that Amritdhari person is sikh but what name will we give to people who are not yet amritdhari but come to Gurdwara assuming they are sikh. If you ask them they say they follow sikhism obviously definition of Sikh is different for them.

A Gursikh/Sikh is someone who has taken Amrit and made an oath to
live their life in accordance to Guru Sahibs teachings.
If person does Gurmat activities but has not taken Amrit
then they are generally known as a " Nigura" "Veymukh"
or "Manmukh". If a person takes Amrit but doenst follow
Gurmat then he or she is a manmukh. If a person commits
a bujjar kurehit then he is a veymukh and nigura and can only be
Guru Ka Sikh after peshing.

If someone is living in accordance to Gurmat and are planning
to take Amrit at the next Sanchar then they are
generally referred to as" KeshDhari", "SehajDhari"
"ShardaLoo", and "Abhilakhee".

Sikh Reht Maryada

SIKH CODE OF CONDUCT AND CONVENTIONS
Section One


CHAPTER 1
The Definition of Sikh :

Article I
Any human being who faithfully believes in
i. One Immortal Being,
ii. Ten Gurus, from Guru Nanak Sahib to Guru Gobind Singh Sahib,
iii. The Guru Granth Sahib,
iv. The utterances and teachings of the ten Gurus and
v. the baptism bequeathed by the tenth Guru, and who does not owe allegiance to any other religion, is a Sikh