Strictly speaking, a boundary is a visible mark which shows or sets a bound or limit.
The distinction can be clearly seen in the historical development of the word, which was formed from bound (“limit”) plus -ary (“connected with, pertaining to”). (OEtmD)
However you do not normally see this distinction made between boundary and bound or limit except in formal, technical contexts such as the law. In common, idiomatic usage, boundary often means bound or limit.
The idiomatic usage of boundary is nothing new. Consider the lexicographer’s complaint from the 1828 Webster’s Dictionary:
This word is thus used as synonymous with bound. But the real sense is, a visible mark designating a limit. Bound is the limit itself or furthest point of extension, and may be an imaginary line; but boundary is the thing which ascertains the limit; terminus, not finis. … But the two words are, in ordinary use, confounded.
Here, from the Macmillan Dictionary, are two sentences in which boundary is used in a sense which is not easily interchangeable with limit:
- The boundary between fact and fiction in her writing is often blurred.
- The Una River forms a natural boundary between the two countries.
And here, from Shakespeare courtesy of the 1913 Webster's Revised Unabridged Dictionary, are three sentences in which limit is used in a poetic sense not easily interchangeable with boundary, to mean not the bound but the entire space or time delimited:
- The archdeacon hath divided it / Into three limits very equally.
- The dateless limit of thy dear exile.
- The limit of your lives is out.