Presumably the order is to get "entry clearance", then achieve "leave to enter" the country, with a later application for "leave to remain", once you are in the country.

LTE is given at the airport on entry if you are not a visa national. If you are a visa national or are entering in a visa mandatory category and you have a UK EC (visa) then you already have LTE as an EC is LTE. LTR is given by the Home Office after a successful application to extend existing LTE.

leave to enter is the same as entry clearance.

there are two types of leave to remain:
1 limited leave to remain (you will be notified how long this is and if/how you can extend it)
2 ILR (indefinate leave to remain) this means you can remain in the country, go out and come back without hindrance

there are now two types of student visa – see link – both give leave to enter with limited leave to remain.