The verbs in each case are different verbs.
Ps 48:9
Here the operative verb is דָּמָה (damah) whose meaning is (according to BDB) is:
1 liken, i.e. consider to be like, compare, causative of
Qal followed by לְ of external appearance Songs 1:9; of quality or
condition Isaiah 46:5 (object ׳י) Lamentations 2:13; followed by אֶל
of external appearance Isaiah 40:18,25 (both object God in reference
to idols); absolute use comparisons or similitudes (parables, symbols,
etc.) Hosea 12:11 (subject ׳י).
2 imagine, form an idea, devise 2 Samuel 21:5 (on context compare Dr);
think, intend, followed by Infinitive Numbers 33:56 (J or H) Judges
20:5; Esther 4:13; absolute Isaiah 10:7; compare Isaiah 14:24; think
that, followed by object clause (Imperfect without conjunction) Psalm
50:21; think of, followed by accusative Psalm 48:10. Hithpa`el make
oneself or become like; Imperfect אֶדַּמֶּה לְעֶלְיוֺן Isaiah 14:14 I
will make myself like the Most High (on form compare Ges§ 54. 2).
That is, the central idea is to "think about or consider, ponder, plan". and thus included "meditation".
Ps 104:34
The operative noun here is שִׂיחַ (siach), which means (according to BDB):
שִׂיחַ noun masculinePsalm 104:34 complaint, musing; — absolute ׳שׂ 1
Kings 18:27 Proverbs 23:29; suffix שִׂיחִי 1 Samuel 1:16 +, שִׂחִי Job
23:2, שִׂיחוֺ 2 Kings 9:11; Psalm 102:1; —
1 plaint, complaint: Job 7:13; Job 9:27; Job 10:1 ("" מר נפשׁ), Job
21:4; Job 23:2; Proverbs 23:29; Psalm 55:3 ("" אָהִימָה); קוֺלִי
בְּשִׁיחי Psalm 64:2; ׳לפני י ׳שָׁפַךְ שׂ Psalm 102:1; Psalm 142:3.
following are dubious:
2 musing, 1 Kings 18:27 (E) of a god, "" שִׂיג לוֺ, (so RV; SS
'nachdenken'; Buhl 'beschäftigt sein'; AV talk); Psalm 104:34 of man
(Buhl SS. Bae 'Rede, oder Gesang').
CONCLUSION
Thus, the cognate meaning of these two words can overlap at the place where both mean to think upon, ponder. This idea of meditating on the goodness and love of the LORD appears in many places such as:
- Ps 19:14 - May the words of my mouth and the meditation [ הִגָּיוֹן ] of my heart be pleasing in Your sight, O LORD, my Rock and my Redeemer.
- Ps 49:3 - My mouth will impart wisdom, and the meditation [ הָגוּת ] of my heart will bring understanding.
- Ps 39:3 - my heart grew hot within me. While I meditated [ הָגִיג ], the fire burned; then I spoke with my tongue:
- Ps 77:6 - I remembered my songs in the night. My heart meditated [ שִׂיחַ ] and my spirit asked ... [See also V3, 12.]
- Ps 143:5 - I remember the days of old; I meditate [ הָגָה ] on all Your works; I consider [ שִׂיחַ ] the work of Your hands.
Thus, several Hebrew words are used to describe meditating, musing, considering and pondering.