Most languages have a way to signal a generic error with a string as the error message. This makes it easy to include relevant information in the description of the error: something as simple as (error "serve-ice-cream: quantity=~S must be positive" q) provides a human-readable description with whatever information you think is relevant. It's not machine-readable, but most errors don't need to be handled mechanically, so this is not usually a problem.
Languages with exception systems also allow signalling errors in a machine-recognizable way, typically by defining a new exception class. This is often considered the “proper” way to signal errors, but it's more work than a generic error, so it's typically done only for polished public interfaces. Errors that aren't exposed in such an interface (or aren't intended to be exposed — errors are a kind of implementation detail that's hard to hide) generally make do with strings.
When you do create an exception class, it's also more work to include relevant information in the exception. Typically you have to define slots, arrange for them to get the appropriate values, and then embed them in the error message. This requires changing several parts of the definition as well as the call site, so it's enough trouble that you often won't do it. Error reporting code is seldom high on the priority list until the error happens.
I ran into this problem a while ago, in a utility function which reported a rare error by throwing a C++ exception class like this:
class negative_error : public domain_error {
public:
not_integer_exn() : domain_error("value must not be negative") {}
};
This was fine until the error finally happened. A high-level catch-almost-anything handler caught the exception and displayed the error message, which told me almost nothing about the problem. Since this was C++ and not running under a debugger, there was no automatic stack trace, and no hint of what value was negative, or who cared, or why. If I had been lazy and signaled the error with throw domain_error("serve_ice_cream: quantity=" + to_string(q) + " must not be negative"), the relevant information would have been in the string, but because I had done it the “right” way, it was not.
(The designers of C++ are aware of this problem. That's why all the standard exceptions take strings. negative_error should have too.)
In an ideal exception system, convenience and machine-readability would not conflict. It should be easy to signal an an-hoc error with a human-readable message and machine-recognizable fields. It might help to allow throwing exceptions without declaring them first, e.g. (throw '(negative-error domain-error) :quantity q "value must not be negative"). (Wasn't this allowed in some early exception systems?) But if it's only easy to have one of the two, choose the convenient human-readable form. That's the one you'll use.