Regarding the definition of 표제, a similar question can be raised for the English word note:
note: something that you write down to remind you of something
why is it "that you write down" not "that you wrote down" or "that you have written down"? I do not know the exact answer, but it seems that the present tense is preferred by lexicographers when it is possible to use either tense, in other words, when there is no reason to use the past tense instead of the present tense.
읊다 has these meanings:
To read or recite a poem, song, etc., with varied intonations.
To poeticize (write a poem about)
읊다 used in 사랑을 읊은 노래 relates to the second meaning. You cannot complete a song before you write its lyrics. Thus, the (relative) past tense seems to be correct to use for the definition of 정가 (a song of which the lyrics you wrote about love).
In general, the past tense in Korean can be the present perfect, past, past progressive, or past perfect tense in English. For your sentences, the two phrases can be either completely different or almost the same.
관심을 가지는 사람 = people who take an interest (Note: You cannot be sure whether they have ever been interested.)
관심을 가진 사람 = people who took (or has taken, had taken, etc.) an interest (Note: You cannot be sure whether they are still interested.)