Lyme is caused by bacteria. Wikipedia says:
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"Borrelia burgdorferi is a bacterial species of the spirochete class of the genus Borrelia.
"B. burgdorferi exists in North America and Europe and is the predominant causative agent of Lyme disease."
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Spirochetes are tiny spiral-shaped bacteria, and Lyme is one kind of spirochete. Borrelia is the scientific family name that includes Lyme, and the formal name for Lyme is 'Borrelia burgdorferi' -- the bacterial family name is 'Borrelia', of which there are several subcategories including Lyme. The scientist who discovered the Lyme bacteria is Willy Burgdorf, and his name was given to it.
It's like car names:
Chevy Suburban
Borrelia burgdorferi
More than you ever wanted to know, eh?
So is it actually bugs or just bacteria?
It's just a silly way to refer to the Lyme bacteria. I sometimes spell it 'bugz' just to show the creatures that we laugh at them! :D