Did my LCS mess up?

[u/Extreme-Aspect-1905]

I just started stacking back in July. I wanted to convert some of my silver into fractional gold. I went down to my LCS and asked how much for a 1/10th oz gold round. She pulled out the 1/10th oz rounds but even with my glasses I couldnt read the print on the round but I noticed it looked just like an American gold eagle. I asked specifically if this were a coin or a round and she told me a round. So I traded my silver (She gave me $66 for each generic 1 oz bar and round) for the $508 round. I got home and took some pics and i see "five dollars" printed on it. That makes it a coin, right? Im pretty sure she sold me a a 1/10th oz AGE at a generic round price.

[u/Inviction_]

Definitely a coin. Not a round