Quite different Hebrew verbs are used in Gen 1:20 and 24. Let me be more specific (my translations).
- Gen 1:20 - "And God said, let the water abound with an abundance of living creatures ..." The Hebrew verb here is שָׁרַץ (sherats) meaning "to swarm, team", (BDB). See also Gen 1:21, 7:21, 8:17, 9:7, Ex 1:7, 8:3, Lev 8:29, 41, 42, 43, 46, Ps 105:30, etc.
- Gen 1:24 - "And God said, let the earth bring forth the living creature ..." The Hebrew verb here is יָצָא (yatsa) meaning (BDB) "to go or come out, com forth". See Gen 1:12, 24, 2:10, 4:16, 8:7, 16, 17, 18, 19, 9:10, 18, 10:14, 11:31, 12:4, 14:8, 17, 18, etc.
It is also clear that when God created He was not necessarily dependent on pre-existing matter (Which He had previously created anyway). However, that is the method God chose to use in the case of Adam (Gen 2:7 using yet another verb).
The sense in Gen 1:20 and Gen 1:24 is not that God used the water or the earth to make the creatures but simply that is where is brought them forth or placed them.