Yes, ”the” is essential in forming this sentence. That's because "We're afraid of others" would be translated as: ”Ne este teamă de ALȚII”.
CELĂLALT (sg. masc.), CEALALTĂ (sg. fem.), CEILALȚI (pl. masc./a group where there's at least one man), CELELALTE (pl. fem.) are demonstrative pronouns of differentiation, which means they show objects which are different or the same with an aforementioned object. These are definite.
ALTUL (sg. masc.), ALTA (sg. fem.), ALȚII (pl. masc.), ALTELE (pl. fem.) are indefinite pronouns.
They are synonymous with each other. To me, frică is a bit ( like, very, very, very little) stronger than teamă, but aceasta este doar o nuanță (this is just a nuance) which could be explained by the idioms used by my family growing up, and can easily be different for others. Feel free to use either interchangeably in any context!