Many languages distinguish, including people considering it offensive if one uses the wrong word. For example in German, an animal can "frisst" while I human would "isst," because beasts eat differently from civilized humans. English doesn't have the distinction, but many English speakers do distinguish between the biological meaning of animal and the "practical" meaning. So, having two words helps convey that thought process.
This appears to be a reference to what I say here:
and "bestaĉo is indeed a nasty animal, but that's not quite what beast means."
"Animalo" is a scientific word - it's means a member of the biological class animalia. Here's the definition in PIV: "Eŭkariota vivulo (ss plurĉela, vs k ark. ankaŭ unuĉela) sen klorofilo, kies ĉelmuroj ne konsistas el celulozo, ĝenerale kapabla senti k sin movi; kn de bestoj k homoj." "Besto" is the normal word for animal in Esperanto. Here are the two definitions from PIV: "1 Ĉiu animalo escepte de homo. 2 Homo stulta aŭ kruda kiel besto." Note that the word "besto" belongs to the Fundamento de Esperanto, while "animalo" was only recognized by the Academy in 1974.