The main difference between mochi and dango is this: mochi is made from grains of steamed rice, while dango is made from rice flour. That said, as I mentioned earlier, many modern mochi are made using rice flour. This results in a different texture, and you could make the argument that what they're making is actually dango. But at the end of the day, it's all delicious, so who cares.
Two popular types of Dango you're likely to see in Japan are mitarashi dango and hanami dango.
This traditional Japanese sweet originated in Kyoto. Its name "mitarashi" comes from the word for the purifying fountains placed outside Shinto shrines. It's made by grilling 3-5 dango on a skewer and coating it in a thick, sweet soy sauce glaze. Nowadays, mitarashi mochi can be found throughout Japan, from street stalls to convenience stores.
These cute rice cakes are especially popular in the early spring for the sakura flower-viewing season, though they are available all year round. They're so iconic that there's even an emoji for them [🍡]. They are almost always served as 3 dumplings on a stick. Pink represents the cherry blossom flowers, white is for the remaining winter snow, and green for the coming spring grass.