# [Charcoal], 29 bytes

    ∧⁼§θ⁰§η⁰⁼↧⪫⪪⪫⪪θ_ω-ω↧⪫⪪⪫⪪η_ω-ω

[Try it online!][TIO-j5nku8m5]

[Charcoal]: https://github.com/somebody1234/Charcoal
[TIO-j5nku8m5]: https://tio.run/##S85ILErOT8z5//9Rx/JHjXsOLT@341HjBiC1HUgBBR61LX@0avWjVasg5Lkd8ec7dc93ogtvhwj//58YlliUmZiUk@qXmJuqkBhfBuXq5gH5AA "Charcoal – Try It Online"

This prints a `-` for truthy and nothing for falsey.

Link to the [verbose version][1]. It first compares the first character of both input strings (`⁼§θ⁰§η⁰`) and then compares the rest of both strings after removing the underscores and the hyphens (`⪫⪪⪫⪪θ_ω-ω`) and converting to lowercase (`↧`).


  [1]: https://tio.run/##hYuxCgIxEAV/JaTaQAL2VldYKCKCYHusuUACMfGSePHv1y1OsBB81Qy8sR6LzRiJziWkBkOaYDc/MVYY2j5N7gWz3ij9Ec@itFgvx9xdsVgdHHJIcHnE0L5x1kKOUunOiTQMonP9r/K/Kt6WCK9YAt6iO@HdCRyXVU1iJ7OQqfEN