Both words refer to something that is readily apparent or easily perceived or sensed. As an adjective, clear has a wide range of reference: from materials (clear glass) to communication (a clear explanation). The relevant sense here describes something that is apparent, obvious, or easily perceived or understood: the team’s clear sense of pride. Palpable is a more emphatic, even dramatic word for something easily perceived, because of its literal meaning—able to be touched or felt—and its usual application to things like a mood, emotion, or atmosphere, which are insubstantial and can’t be touched. It suggests that an emotion or mood has such a strong presence that it is like something solid and material. The frequent use of the phrase almost palpable draws on both definitions of the word to make this point.
Both words refer to being keenly aware and attentive to one’s surroundings or the activity one is engaged in. Alert suggests being fully awake and aware and thus capable of quick perception and reaction: stay alert while driving; only alert readers noticed the error. Vigilant suggests a more consciously sustained watchfulness, for the purpose of detecting danger: we must remain vigilant until the threat has passed. It commonly modifies citizens, neighbors, and guards, as well as processes like enforcement, monitoring, and oversight.
Skillful and adept refer to being very proficient at something requiring quickness or agility of body or mind, through natural ability, training, or practice. Skillful often, but by no means always, suggests physical adroitness and dexterity: skillful hands. It is often applied to a person in a defined role or to the activity done well: a skillful player; skillful performance. Adept is a strong synonym for skillful and will work much of the time. Adept is more often used to describe a person who is adept at doing or achieving something that may be very particular rather than expected in a certain occupation or profession: adept at identifying the right person for the part.