The confusion here is probably caused by the choice of although (instead of but) as a translation of -(으)나.
My guess is DLG wants to point out the grammatical difference between -지만 and -(으)나, namely the order of the 2 linked clauses.
배 안 고프지만 먹는다 - I am not hungry, but I eat.
[Despite being attached to Clause1, "but" defines Clause2 ~ similar to English ]
배 안 고프나 먹는다 - I eat, but I am not hungry.
["but" defines Clause1]
It feels difficult sometimes for learners to follow the logic without proper notes. But the main difficulty (I find) is to try to get away from the literal translation mindset ...
(1) 먹다 [=, to eat] is the dictionary or "basic" verb form, used for referencing.
먹는다 [= eat(s)] is the "conjugated" form of 먹다, used in
• the present tense;
• in a declarative type (statement),
• in plain style (also called report/diary style)*
먹었다 • past tense = ate
먹을 거다/ 겠다 • future tense = will eat
• the basic form -다 is never used in conversation unless the verb is a descriptive/adjectival verb.
• the plain form -ㄴ/는다 on the other hand seems to get used more frequently nowadays by the young generation in casual conversations with close friends. (An alternative to the laxed/intimate 어 verb ending)
• Also ways use 나 (= I) with verbs in plain form.