My first thought was the People series by Zenna Henderson. I was unable to find a matching cover but part of the plot involves a ship coming from a safe planet to rescue those aliens (basically humans with psychic powers) who had crash landed on Earth. This gives you both the original Earth crash as well as the controlled but rough landing of the rescue ship. On the ship is a girl who sneaks out to experience Earth guided by a boy born since the original crash. The psychic abilities are developed enough to resemble advanced technology in some cases.
Most of her stories emphasize the theme of being different and the dangers therein, exemplified by the phrase "Different is dead". They often feature children or young people. Most are part of her series concerning the history of "The People", humanoid beings from a faraway planet who are forced to emigrate to (among other places) Earth when their home world is destroyed by a natural disaster. Scattered mostly throughout the American Southwest during their landing before 1900, they are set apart by their desire to preserve their home culture, including their religious and spiritual beliefs. Their unusual abilities ("Gifts") include telepathy, telekinesis, prophecy, and healing, which they call the "Signs and Persuasions". The stories describe groups of The People, as well as lonely isolated individuals, most often as they attempt to find communities and remain distinct in a world that does not understand them.
While it is never explicitly spelled out in the stories, it is mentioned that very early in the history of The People, they had an expansive, colonial phase, and spaceflight had to be Remembered when the destruction of Home was prophesied, so Earth's humanity may well be their distant cousins. This would explain the similarity between the two species.
Beginning with "Ararat" (1952), Henderson's The People stories appeared in magazines and anthologies, as well as the novelized Pilgrimage: The Book of the People (1961) and The People: No Different Flesh (1966). Other volumes include The People Collection (1991) and Ingathering: The Complete People Stories (1995)