We prefer literal translations of whole blocks rather than individual words, if at all ;) E.g., while «на улице» can mean "on(in) the street" sometimes (namely, when you talk about streets), it is also very often used as "outside" and "outdoors" (which makes much more sense in this sentence).
One phrase for "outside" is much easier to remember! In English when we talk about outside we often specify where we are outside too - outside: in the park, in the woods, in/on the street, your house. Just "outside" is good when you don't want to say exactly where outside!
"On the street" can be used for "outside" in American English, but I think frequently this would be used as a way of communicating "outside" in the context of describing someone living outside - like a person without a house or apartment, or a feral cat. This is adjacent to how "on the street/in the streets" can be used to describe somebody surviving by means of doing illegal or unsavory business with strangers and all manner of dangerous characters (still usually without a safe place to live). Depending on the context, the living outside/without shelter bit may or may not be the point.
Fun fact: in Polish, to say that we are outside, we usually say "na dworze", which translates literally as "on the court". Except in Cracow, where they say "na polu", which means "on the field". I guess us Slavs just go outside so rarely that we have a hard time figuring out where we actually are.
While "снаружи" is used as an adverb for both "on the outside" and "from the outside", "наружу" may be better for simply "outside", although it can also mean "on the outside" or "to the outside". "вовне" is the simplest adverb for outside, while "на улице" and "на дворе are colloquialisms.