Correct definition of terminal alkynes? My textbook, Organic Chemistry (6th edition) by Brown, Foote, Iverson, and Anslyn, states:


  Alkynes in which the triple bond is between carbons 1 and 2 are commonly referred to as terminal alkynes.


Is not this definition incomplete? I can imagine scenarios where we have a terminal triple bond that does not reside between carbons 1 and 2 according to IUPAC rules. E.g., $\ce{CH2=CH-C#CH}$. Here, the terminal triple bond is between carbons 3 and 4 (according to IUPAC rules, doubles bonds take priority when numbering).
You are correct about the absolute numbering of $\ce{CH2=CH-C#CH}$. By the IUPAC priority rules, the alkene has the lower absolute numbering.
However, numbering can also be relative. In your case, the relative numbering 1,2 refer to either of the following:

relative position from the end of the chain, where the chain end is #1
relative position from the functional group you care about (where that group is #1)
suggesting that a reaction occurs on neighboring positions in a molecule.

That being said, the definition given by Brown et al. is imprecise. A better definition is one of the following:

A terminal alkyne is an alkyne in which one (or both) of the two alkyne carbons is at the end of a chain.
A terminal alkyne is an alkyne $\ce{RC#CR}$ in which one or both $\ce{R}=\ce{H}$