We are beginning siman 9. The Chayei Adam writes that a small fish which is already in a small area, and a person uses a net to catch it, they are chayav. Although it is already a small area, since the fish is not easily captured, using a net is a melacha deoraysa. Similarly, any time an animal is in a large enclosed area and a person wishes to move it to a smaller enclosure, if the large enclosure is large enough that the animal cannot be captured in one chase, and in the smaller one it can be caught in one chase, it is assur miderabanan.
When it comes to fish, besides for tzad, removing the fish from water is considered shocheit. Even though the person is not actively killing it, removing it from the water is considered killing it. To explain, if a person puts another person into a room with no air, the assailant cannot claim that the lack of air killed the victim and not the assailant, because the assailant put the victim in the room. In a similar sense, although the lack of water is what kills the fish,the person who removes the fish from the water is considered to have killed it.
If a person has a fish tank and one of the fish dies, there is an issue of muktzah to remove the fish. Assuming for a moment that we can avoid the muktzah angle, there is no issue of shocheit to use a net to move the live fish elsewhere, because the person’s intention in moving them is not to kill them. However, the melacha of tzad will still apply (assuming the tank was large enough that the fish could not previously be caught in one chase). In that situation, using a net to remove the fish is considered tzad, even if it is only temporary. It could be argued that it is a melacha she’eina tzricha legufa, because the person is not trying to capture the fish inasmuch as to clean the tank. One should consult a rav.
Summary
Trapping animals that were already in an enclosure, but in the previous enclosure they could not be caught in one chase, is considered tzeida mideoraysa. Examples include catching a small fish with a net even if it was previously in a relatively smaller area.
If a fish died in a fish tank, and the person wishes to move the remaining fish, they should consult with their rav.