I tend to use the words define, declare and assign interchangeably but this seems to cause offense to some people. Is this justified? Should I only use the word declare for
It might depend on the language, as has been said. I think it really depends on whether the words are used for things like classes. For most of the data types discussed here, the question might not have much relevance. In C++ (see c++ - What is the difference between a definition and a declaration?), a class or struct always has precisely one definition but can be declared zero or more times. A class cannot be declared without a definition. So "declared" might be synonymous with "used".
In most languages, simple types such as integers do not need definitions in the manner that classes do.