Super similar instruments indeed.
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They're not even part of the same instrument family.
If she wanted her lie to have been remotely believable she should have claimed to have played saxophone and clarinet. As it's relatively easy for someone skilled in one of those instruments to play a tune on the other.
I suspect she heard of someone playing
english horn as well as saxophone. And decided to pretend to have that achievement. Unlike french horn which is a brass instrument; english horn is basically a oboe and somewhat similar to a saxophone in how it's gripped, but not as close as a clarinet, and the mouthpiece/reed is much more different too.