Terry,
If you want to see Korean forms that are similar to Shotokan forms, you can check out a school from one of the old kwans that had schools that remained independent when TKD was created. For example, certain Ji Do Kwan or Moo Duk Kwan schools.
There are many Ji Do Kwan forms that have almost exact parallels in Shotokan. For example, Shotokan Taikyoku = Ji Do Kwan Ki Cho; Shotokan Heian = Ji Do Kwan Pyung Ahn; Shotokan Bassai Dai = Ji Do Kwan Bal Sak Hyung; Shotokan Kankudai = Ji Do Kwan Kwan Kong Hyung. There are several more (Shotokan Tekki = Ji Do Kwan Cholgi...).
Sorry, but I'm completely unfamiliar with the Taegeuk forms, so I can't compare them to Shotokan.
Hope this helps.