Ahmadi vs Qadiani
Ahmadi and Qadiani are essentially different names for a same islamic movement.
Hazrat Mirza Ghulam Ahmad Sahib was the founder of Ahmadi Movement.
According to the Ahmadi sect believes that all those who have read ‘Kalimah-e-Tayyebah’ are Muslims, irrespective of the sect that he or she belongs to and also even if he has not taken the pledge of Founder of Ahmadi. The Ahmadi sect believes that non-belief in Mujaddid (Promised Messiah) is a sin. Moreover, no one is thrown out of Islam and no one becomes Kafir if he has committed a sin.
Ahmadi sect has their headquarters in Pakistan.
In Islam, there is a prophecy about coming of a spiritual reformer in latter days with two titles. One is Promised Messiah and other is Mahdi.
Ahmadi Muslims believe that both titles belonged to one person, subservient to Holy Prophet Muhammad. They have their full arguments. They believe the reformer will stop use of force for religion as it was foretold.[Non-Ahmadi Muslims are waiting for two separate men; one as Promised Messiah and second as Mahdi. Mahdi will shed blood.]
After the death of Ahmadi Promised Messiah, Hazrat Mirza Ghulam Ahmad (on whom be peace) in 1908, a system of Khilafat (successor-ship) started [as per prophecy of Holy Prophet Muhammad (pbuh)].
Their head office remained in Qadian (India). Those who thought, Khilafat was not needed, they went to Lahore (then India, now in Pakistan)
Both types are called Ahmadis because they Hazrat Mirza Ghulam Ahmad (a.s.) gave the name of his Community as Ahmadiyya Muslim Community.
At maximun, one can say:
1- Ahmadi Muslims (who follow Khilafat; currently Fifth Khalifah is heading the worldwide community)
2- Ahmadi Muslim (who do not believe in Khilafat, they are much lesser, they are called LAHORI GROUP)