Both words refer to someone who puts on a false or deceptive appearance or persona. Fake is the broader term. It covers all phonies—the insincere, the pretentious, and the outright deceitful. A charlatan is someone who poses as an expert in some area of knowledge and uses their charismatic gifts in order to sell a bogus miracle product—whether it’s the proverbial medicinal snake oil or political promises. Charlatans typically connive, thieve, and peddle. The word frequently appears in the company of words for exposing someone as a charlatan, such as demask and debunk. Publicly calling someone a charlatan is also newsworthy.
Small is a fairly neutral word to describe an amount that is not large. To let someone know how you really feel about such an amount, you could qualify small with “ridiculously” or “insultingly”—or you could capture all that information in one word, namely, paltry, which suggests a very small, insignificant, or inadequate amount. By far the most frequent application of paltry is monetary: a paltry sum, amount, or salary, although there might be paltry attendance at a poorly publicized event, or, if you have nothing better to complain about, a paltry serving of caviar. The paltriness of something often emerges comparatively: The other late night show had a comparatively paltry 89,000 viewers for its holiday special.
Both words describe a person or thing widely known and (usually) admired. Famous can be applied to anything widely known or “heard of” by many: it most frequently describes actors, artists, and writers and other popular figures. Famous can sound a little shallow and incongruous when used to describe people known and admired for serious accomplishments or contributions. This creates an opening for renowned, which suggests being held in high esteem and celebrated by many, and is usually used for what could be considered more serious accomplishments. You’ll find it used of actors, artists, and writers, but also of experts, architects, professors, economists—and other professions whose expertise is not given a great deal of notice in popular or mass culture.