It was a question I was asked by my American friend when I guided her in spring and I thought it was an interesting question that shows a cultural difference.
Yes, actually most Japanese people can tell which flowers are cherry blossoms and which are not immediately although there are several similar flowers, like plum flowers and peach flowers, blooming in the almost same season.
For one thing, it is because cherry blossoms are the most popular flower among Japanese people and every spring people have gone out for “cherry-blossoms-viewing” since their childhood, so people have enough experience to learn about the appearance.
But actually we can tell not only cherry blossoms. When Japanese people go out for a flower-viewing picnic/excursion we usually aim for one particular kind of flower. It can be any kinds of flower, but we wouldn’t aim for unspecified seasonal flowers. With this cultural background, most Japanese people can identify famous seasonal flowers. I guess many examples of traditional art, drawings and designs also help people to recognize each kind of flower.
For example, there have been many traditional family crest designs based on cherry blossoms and plum flowers. I'll show some of them here. The left row is cherry blossom designs, and the right row is plum flower designs. I think it shows very well how Japanese people recognize which one is which between the two kinds. They can’t be completely accurate standards since there are so many varieties of both kinds, but it still can help tell the typical difference between those.