Chamomile can refer to a number of different plants; all are daisy-like plants in the composite (daisy) family; it normally refers to German chamomile, Matricaria recutita. This is the species typically used in chamomile tea.
Roman chamomile, Anthemis nobilis, is a similar plant; it is less often consumed as a tea, but it is sometimes used for medicinal purposes.
There are several other plants occasionally bearing the name "chamomile".
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Best to my knowledge there is no difference apart from the spelling. They both refer to daisy-like plants of the family Asteraceae.