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.
Grace and poise refer to a pleasing quality of ease and self-control in the way a person moves, carries themselves, or conducts themselves. Grace suggests these qualities enhanced by elegance, dignity, or beauty: a catlike grace; withdraw with grace. Poise emphasizes composure, self-control, and calmness in deportment and manner, more than elegance or beauty. Many of the same verbs are used with poise as are used with “balance.” People lose, maintain, regain, and recover their poise in challenging situations. As a personal attribute, grace goes a little deeper, as it involves generally prized values, such as fairness and good temper, whereas poise is pleasant and admirable for being presentable and smooth.