These two are certainly the most popular. Further... they aren't just popular with the users of the software, they're also popular with the developers of plug-ins. You'll also find many (and probably most) online tutorials show you how to do adjustments to photos... in Lightroom or Photoshop.
BTW, Parker made a comment about the $10/month - Adobe has a subscription model to allow you to use both Photoshop and Lightroom for $10/month provided you sign-up for a minimum 1 year subscription. However, they'll also sell a perpetual license. I think Lightroom is about $150 for a perpetual license.
If you shoot RAW (and even if you don't... if you're serious about photography you'll probably eventually start shooting RAW) then you'll want something that can support the RAW formats of your camera(s).