There are a number of easily confusable words in English, sometimes in speech and often in writing. The differences between aide and aid is very clear once you know it, and the same goes for adopt and adapt.

Aide and aid are often mistaken for one another, simply because they are pronounced the same way and spelled so similarly. However, they are very different, and when you know their definitions the debate of aide vs aid will be nonexistent. Aide is a noun, meaning a helper or assistant. Aid, on the other hand, can either be a verb, meaning to give help or assistance; or a noun, referring to help or assistance given. A nurse’s aide (noun) will give aid (noun) to a patient; she can also aid (verb) in relief efforts.

Adopt vs adapt is a little more subtle, as both are verbs. Adapt can either mean to take something and make it suitable for one’s needs or circumstances, or to alter oneself in order to be better suited for circumstances.
For example, a recent immigrant who fits in to his new culture can adapt, ie. change his actions or speak a new language, or a monkey can adapt a stick to use as a tool.
Adopt means to take something as one’s own. A couple can adopt a baby, or a convert can adopt a new set of religious beliefs.

Although it is easy to see why these words are confused, it is equally easy to tell them apart when you know what they mean.