Translation:No, ants are not bugs either, but insects.
In strict biology terms, a bug has a specific type of proboscis, more specifically, a member of order Hemiptera. Sometimes the term true bug is limited further to the order Heteroptera, which has a specific wing structure.
That said, the English term "bug" is used in the colloquial language to refer generically to any insect or creepy-crawly, sometimes including even spiders and worms.
Question for native Hungarian speakers: Does the Hungarian term bogár similarly refer to any creepy-crawly? It appears that, in biology contexts, HU bogarak == LA coleoptera == EN beetles. Meanwhile, EN bugs (in the specific sense) == LA hemiptera == HU poloskák. Is poloska ever used colloquially to refer to any creepy-crawly?
"Is poloska ever used colloquially to refer to any creepy-crawly?"
Nope, poloska is a specific type of insect. There are two types: mezei poloska: shield bug. Also called büdösbogár (smelly bug/stink bug)
ágyi poloska: bedbug
Or, a poloska can be a wiretap (small device someone secretly put in your home to listen to your conversations).
Yeah, it would be more correct to say "not beetles but insects". Although it could be argued what exactly "bugs" mean.