Examples of non trivial ordering relations , I mean ordering relations without apparent comparative term in their definition. As an example of ordering relation that do not contain a comparative term ( such as " is greater than") in its definition, I can find " set X is included in set Y". But it seems difficult to me to find many other examples. Can you think of many relations that are orderings but do not contain any apparent comparative term in their definition?

The relation on the integers given by "$a$ divides $b$" is an order relation that does not seem to be described by a comparison operator.

You might say the same about the relation on people defined by "ancestor of". Whether that counts depends on whether you think of "ancestor of" as a kind of comparison.

As discussed elsewhere in this question, there is always a comparison, which may be more or less explicit.