You are correct, the word "subject" has different meanings depending on the context. But that is not at all unusual, especially in English, which borrows so much of its vocabulary from other languages.

Very well. I just find it odd to find such potentially misleading terms in a field that attempts to have clear and distinct ideas. Thank you.

I don't see any inconsistency between the grammatical and the non-grammatical senses of 'subject' and 'object'. The sentence 'The ball is red' does not imply that the ball is observed (for instance it could have been painted red while in a totally dark room), so it does not imply that the ball is an 'object' in that non-grammatical sense. A sentence in which the ball is observed is 'I looked at the ball'. In that sentence 'I' is the grammatical subject and 'ball' is the grammatical object, which is consistent with the other meaning of 'object' as something that is observed.

There are definitely interesting things to be said about the relationship between the metaphysical subject/object distinction and the grammatical subject/predicate distinction -- not least that the copula 'is', which links subject to predicate, has often been understood to have a special bearing on the metaphysical notion of being.

Speaking very roughly, Aristotle held that the ultimate metaphysical objects are those which are never found in the predicate position of any true judgment (e.g. "the statue is the clay"); they are only ever the subjects of judgment (e.g. "God is all things").

Kant, likewise, held that because every judgment is issued by a thinker, the true grammatical subject of every judgment (e.g. "the table is brown") just is the metaphysical subject, or self (e.g. "I think the table is brown"). Philosophers have had a lot to say about these ideas.

Maybe the term 'observed' by itself was misguiding in the first meaning. I should say that the object is the thing either observed, or discussed, or thought of, or in other words, the object of knowledge. Respectively then, the subject is the observer, or the speaker, or thinker, or in other words, the thing that knows the object.

Thus when I see or say or think "the ball is red", then the ball is the object, and I am the subject.

Speaking very roughly, Aristotle held that the ultimate metaphysical objects are those which are never found in the predicate position of any true judgment (e.g. "the statue is the clay"); they are only ever the subjects of judgment (e.g. "God is all things"). — Glahn

That makes sense to me. The relationship between subject and predicate can be seen as a master and slave relationship, in that order. Thus the subject is greater than its predicate. On a similar note, I heard from a christian philosopher that we should never say "God is like X", but should rather say that "X is like God", because God is not mimicking anything, and rather, things are mimicking parts of God.