What is the exact difference between Muslims and Islamic people?

Islam (n) is the religion preached by Mohamed

Islamic (adj) is the adjective that means: related to Islam.
Muslim (n) is a person who follows Islam

Today, the word Islam refers to the religion or faith, and the word Muslim refers to one who identifies as someone who practicecs Islam.

In the past - when Muhammad was alive - the term muslim was a generic word that just means “one who submits to God” and in that sense, any monotheist was called muslim and islam was also a generic word that means “submission to God.”

“In other words, muslim in Qur’anic usage means, essentially, a committed monotheist, and islam means committed monotheism in the sense of submitting oneself to God’s will. This is why Abraham can be considered, in this Qur’anic verse, a hanif muslim, a “committed, monotheistic hanif.” As used in the Qur’an, then, islam and muslim do not yet have the sense of confessional distinctness we now associate with “Islam” and “Muslim”; they meant something broader and more inclusive and were sometimes even applied to some Christians and Jews, who were, after all, also monotheists (Q. 3:52, 3:83, and 29:46).”
- Fred Donner (Professor of Near Eastern History – University of Chicago), (Muhammad and the Believers: At the Origins of Islam, 71)

“Throughout this work, I have translated the terms muslim and islam in accordance with their original connotations, namely, “one who surrenders [or “has surrendered”] himself to God”, and “man’s self-surrender to God”…It should be borne in mind that the “institutionalized” use of these terms — that is, their exclusive application to the followers of the Prophet Muhammad — represents a definitely post-Quranic development and, hence, must be avoided in a translation of the Quran.”- Muhammad Asad, (The Message of the Qur’an: Translated and Explained by Muhammad Asad, Gibraltar 1984, 885, n. 17)