The other answers here are quite good, so I won't duplicate them, but I would like to add some context around the word "boss" in English, which has additional connotations — additional meanings that you may want to be careful around.
Boss is a noun, meaning "the person in charge of something," but it can also be a verb — he bossed me around yesterday — and it can also be an adjective — that bossy lady at dinner argued with the waiter the whole night.
What you'll note about the other two forms, the verb and the adjective, is that they both have negative connotations — they're used in cases where someone is claiming authority that they might not rightly have earned. The negative connotations carry into the noun form as well: The noun boss in English often has a subtle negative connotation to it, not just "the person in charge," but "the person who tells me what to do all the time and takes away my freedom." You'll hear sentences like my boss was pretty rough on me today, and my boss is a real hard-ass, both directly implying that the boss was not just managing the speaker, but treating the speaker very badly as well.
You can also see that negative connotation in sentences like he's actually a pretty good boss, or actually I really like my boss, both of which have the speaker showing that in that exceptional case, the word "boss" is intended to have a good connotation. The speaker is speaking casually but still wants the listener to know that boss isn't bad in their context, implying that it's generally bad in most other contexts.
You'll also find situations where the connotation of "person who makes all of the decisions, depriving others of their freedom" is intentional. For example, Boss Tweed controlled nearly all politics in New York City in the late 1800s — if you wanted any role in government at all, you needed Boss Tweed's blessing. Boss Hogg from the Dukes of Hazzard TV show went by that title to imply that he (the county commissioner) was in charge of everything in Hazzard County. Gangsters and mafia members and gang members may sometimes refer to their leader as "Boss" — note the capitalization, implying that it's not just a noun but a proper noun, a name, a term of respect, indicating that the speaker recognizes and likes that authoritarian leadership.
Importantly, what all of these forms have in common is a power disparity: A manager or supervisor may be a colleague or friend, but a boss is usually not. The word boss implies that a person has power and control in a way that the other words don't state as strongly, and a difference in power can often be negative: Hence the frequent negative overtones in the word boss. Notice that I'm worried the boss will fire me is a common English sentence; but I'm worried the manager will fire me is a lot rarer.
Anyway, there's not always a negative connotation to the word "boss," but there's often a subtle overtone of negativity, so in addition to the fact that "boss" is often preferred in more casual contexts than a business setting, you also need to be careful not to imply negativity that you may not intend. So when in doubt, stick with "manager," which is much more neutral.