BORDER and FRONTIER are both lines by which two countries are spearated, but there is a little difference between the two words.
BORDER is a more generalised term which means any line that separates any two regions. Thus we can have the Bengal-Orissa border, or even England-Scotland border, and the like. You may not necessarily need a passport and a visa to cross the BORDER. Also, BORDER has abstract idiomatic usages as shown in the examples below.
FRONTIER is always a guarded border with customs checkings. Passports and visas are always needed to cross a FRONTIER.
BOUNDARY means the dividing line of smaller units of land than the country or the state. It is generally associated with towns, farms, provinces, parishes, counties, districts and so on. In United Kingdom English (the version we use) LIMIT is not equal to BORDER, but in United States, it sometimes means BORDER or BOUNDARY.
1. The West Bengal-Jharkhand border is recently the target of Maoist attacks.
2. The family lived five miles from the Scotland border.
3. As his mother died, Ram almost went to borders of madness in grief.
1. The Pakistan frontier is heavily protected.
2. Minefields and fences are used to guard frontiers.
1. The Ganges is the boundary between Kolkata and Howrah.
2. There was a mango tree close to the boundary of my garden.
LIMIT (AMERICAN ENGLISH)
1. Drive past the city limits.