Good question! The missing bit of information here is that topical steroids are usually not absorbed systemically at high enough levels to cause adrenal suppression. However, they sometimes are. I shall explain.
First of all, regarding the relationship between systemic corticosteroid administration and adrenal insufficiency, please see this answer. The basic idea (which I think you understand) is that exogenous administration of medications that mimic cortisol (a hormone produced in the adrenal gland) suppress the body’s processes for stimulating the hormone naturally. The adrenal gland atrophies due to the lack of natural stimulation. This causes a problem if the medication is suddenly withdrawn, because the body can’t quickly recover the ability to produce cortisol itself. This is called adrenal insufficiency or HPA axis suppression.1
Now to your question:
How do topical steroid withdrawal relate to adrenal insufficiency?
The answer is that if topical steroids are absorbed into the bloodstream at high enough levels for a long enough time to suppress the HPA axis, they will cause adrenal insufficiency. Usually this degree of absorption occurs only with the use of “Group I” topical steroids, the strongest ones. This list shows the different categories of topical steroids by potency. The “super-potent” Group I includes:2
- Betamethasone 0.05%
- Clobetasol 0.05%
- Diflurasone 0.05%
- Halobetasol 0.05%
- Flucinonide 0.1%
The most important factors that determine whether or not HPA suppression will occur are the potency of the drug, the dose, and the duration of use. The Group I agents can cause significant HPA suppression if used for two or more weeks at a dose of ~2g/day. Other factors that predispose to HPA suppression include:
- application to permeable areas (face, mucous membranes)
- occlusive dresssings
- compromised skin integrity
- young age
The first list in your question appears to mostly outline local effects of withdrawing topical steroids. These are possible with less potent steroids and do not require systemic absorption. The second list, on the other hand, describes a syndrome of adrenal insufficiency. These are likely only the circumstances described above.
HPA stands for hypothalamus → pituitary → adrenal, the pathway for producing cortisol.
List was expanded a bit from that link using Bolognia et al., below.
Tadicherla S, Ross K, Shenefelt PD, Fenske NA. Topical corticosteroids in dermatology. J Drugs Dermatol. 2009;8(12):1093.
Walsh P, Aeling JL, Huff L, Weston WL. Hypothalamus-pituitary-adrenal axis suppression by superpotent topical steroids. Am Acad Dermatol. 1993;29(3):501.
Bolognia JL, chaffer JV, Duncan KO, Ko CJ. Dermatology Essentials. Appendix 6: Potency ranking of some commonly used topical glucocorticosteroids. © 2014, Elsevier Inc.
For further reading see:
This powerpoint presentation from the FDA: The FDA Experience: Topical Corticosteroids and HPA Axis
This elaborates on the special problems of the pediatric population and discusses the likelihood and extent of suppression with lower potency steroids.
Gilbertson EO, Spellman MC, Piacquadio DJ, Mulford MI. Super potent topical corticosteroid use associated with adrenal suppression: clinical considerations. Am Acad Dermatol. 1998 Feb;38(2 Pt 2):318-21.