There are indeed clear-cut definitions: there is a difference between what entails disbelief (kufr) versus what entails religious corruption (fisq).
Denial or Disdain
(1) If a Muslim neglects the prayer out of denial of its obligatory status (juhud) or disdain and contempt (istikhfaf), then there is agreement in all four schools that such a person has committed apostasy (with the exception of a new convert who denies obligation out of ignorance).
If such a person became Muslim again, he or she would not have to make up the missed prayers according to the Hanafis and Malikis. According to the Shafi`is, however, such a person would have to make those prayers up, as a disciplinary measure. Both opinions are narrated from Imam Ahmad ibn Hanbal. [Kuwaiti Fiqh Encyclopedia]
The underlying reasoning for this ruling is that the prayer is necessarily known of the religion — anyone who is Muslim knows about the prayer and its obligatory status (aside from new converts, for example). And the very definition of Islam, according to the Qur’an, sunna and consensus of the umma, is “to believe as true all that is necessarily known to have come from the Prophet (peace and blessings be upon him).” [Taftazani, Sharh Aqa’id Nasafiyya]
If one believes in the Qur’an as the revealed word of Allah, and believes in our Master Muhammad as a true prophet, and if something is decisively established as necessarily having come from Muhammad as an obligation of the religion, then that person would surely accept that thing: he would neither deny it nor treat it with disdain or contempt.
As Imam Tahawi states in his well-known creed, “A servant is not considered to have left his faith except by denying that which originally caused him to enter into it,” i.e., except by denying one’s very belief in Allah’s oneness, His books or messengers, or the resulting faith in all that is necessarily known of the religion.
Laziness or Carelessness
(2) If, however, a Muslim neglects the prayer out of laziness (kasl) or carelessness (tahawun), while nevertheless believing that the prayer is obligatory, then he is still a Muslim yet is religiously corrupt (fasiq). In general, Muslims today who neglect the prayer fall into this category, and so by Allah’s grace they are still Muslim.
Such a person must make up all the prayers missed, regardless of their number. There is scholarly consensus on this matter, as mentioned by Imam Nawawi and others.
The same distinction and rulings would apply to other matters of consensus that are necessarily known of the religion, such as fasting, zakat, and hajj.
[Kuwaiti Fiqh Encyclopedia; Nawawi, Majmu`; Ibn Qudama, Mughni]
Allah’s Vast Mercy
Having said the above, one must remember that the doors of repentance and divine mercy are always open: no matter how grave the servant’s crime, even if one of disbelief, the servant can at any time turn back to his Generous Lord and find Him Ever-relenting.
Allah Most High states, “Say: ‘O My servants who have transgressed against their own souls! Despair not of the mercy of Allah: for Allah forgives all sins: indeed He is Oft-Forgiving, Most Merciful.’” (39:53)
And Allah loves for the servant to turn back to Him, as the Prophet (peace and blessings be upon him) explained:
“Allah has greater joy at the repentance of one of His slaves, at the time he returns to Him, than if one of you were on his riding mount in the middle of the desert, only to have it escape from him with his food and drink; so he despairs of it and comes to a tree to recline in its shade, in utter despair over losing his mount, when… Lo and behold! There it is standing right in front of him! So he takes it by the reigns and exclaims out of intense excitement, ‘O Allah, You are my slave and I am your Lord!’ He makes a mistake out of such intense joy!” [Muslim]
And Allah knows best.