Problem Statement

Demonstrate how to compare two strings from within the language and how to achieve a lexical comparison.

The task should demonstrate:

For example, you might demonstrate the difference between generic/polymorphic comparison and coercive/allomorphic comparison if your language supports such a distinction.

Here "generic/polymorphic" comparison means that the function or operator you're using doesn't always do string comparison, but bends the actual semantics of the comparison depending on the types one or both arguments; with such an operator, you achieve string comparison only if the arguments are sufficiently string-like in type or appearance.
In contrast, a "coercive/allomorphic" comparison function or operator has fixed string-comparison semantics regardless of the argument type;   instead of the operator bending, it's the arguments that are forced to bend instead and behave like strings if they can,   and the operator simply fails if the arguments cannot be viewed somehow as strings.   A language may have one or both of these kinds of operators;   see the Raku entry for an example of a language with both kinds of operators.

Let's start with the solution:

compare <- function(a, b)
{
  cat(paste(a, "is of type", class(a), "and", b, "is of type", class(b), "\n"))
  
  if (a < b) cat(paste(a, "is strictly less than", b, "\n"))
  if (a <= b) cat(paste(a, "is less than or equal to", b, "\n"))
  if (a > b) cat(paste(a, "is strictly greater than", b, "\n"))
  if (a >= b) cat(paste(a, "is greater than or equal to", b, "\n"))
  if (a == b) cat(paste(a, "is equal to", b, "\n"))
  if (a != b) cat(paste(a, "is not equal to", b, "\n"))
  
  invisible()
}

compare('YUP', 'YUP')
compare('BALL', 'BELL')
compare('24', '123')
compare(24, 123)
compare(5.0, 5)

compare <- function(a, b)
{
  cat(paste(a, "is of type", class(a), "and", b, "is of type", class(b), "\n"))
  
  printer <- function(a, b, msg) cat(paste(a, msg, b, "\n"))
  
  op <- c(`<`, `<=`, `>`, `>=`, `==`, `!=`)
  msgs <- c(
    "is strictly less than",
    "is less than or equal to",
    "is strictly greater than",
    "is greater than or equal to",
    "is equal to",
    "is not equal to"
  )
  
  sapply(1:length(msgs), function(i) if(op[[i]](a, b)) printer(a, b, msgs[i]))
  
  invisible()
}