Enthnonational conflicts involve conflicts between ethnic nations. In other words, there can be one group that wants a nation controlled by one ethnic group (the ethnic nation) and another group that also wants control, and wants their own ethnic nation. This is common in the middle east right now!
Apartheid specifically refers to institutional segregation based on race, or generally to institutional segregation by some other criteria, such as by sexual orientation. The term comes from Afrikaans, meaning 'separateness'.
"Apartheid" is an Afrikaner term comprised of the Dutch words for separate and hood, which are apart and heid. Together, they mean separateness. Thus apartheid was the South African domestic policy of separateness between white and non-white inhabitants of South Africa. The separateness extended to jobs, housing, communities (non-white workers lived far out from white towns and had to walk miles into town every morning to go to their jobs--streets were daily blocked by the wide swath of non-white workers walking in at dawn and returning at dusk), shops, clothing, opportunities,everything. This policy was so invidious that it extended even to daily courtesies and the commonplace, such as shaking hands, walking on the same side of the street, and speaking the same language: conversations were (perhaps still are) routinely carried on in two languages at once, one speaker using the one, the other speaker using the other.
Apartheid is of course the period of South African rule where blacks and whites were legally separated and blacks had to live a life with a shocking lack of rights and entitlements compared to white South African citizens. It has therefore come to be a term that applies to any policy of racial separation or discrimination.
Apartheid was the policy of racial separation that was part of the official ideology of South Africa when that country was under the control of its white minority. Its chief doctrine was, as the word suggests, to keep the races apart as much as possible. Inevitably it resulted in many disadvantages to the black citizens of South Africa.
Ethnonational conflicts are conflicts between different ethnic groups, particularly when those ethnic groups are competing for control of a state. When one group uses the power of the state to oppress another, that is also ethnonational conflict. An important example of this from recent times is the Tamil-Sinhala conflict in Sri Lanka.