Agastache "hyssop" vs Hyssopus officianalis?

I've been learning about new plants that I have no previous experience with in either my own gardening or as alternative herbal medicinals. But I find I've had a hard time finding information about the differences between the "anise hyssop" which is actually an agastache, and the true hyssopus officianalis, which seems to be of the carrot family. Most websites have not been helpful in telling me that they are in fact different, though are used similarly if not identically. They both also seem to look very similar in their growth habits.

This site ( https://growitbuildit.com/anise-hyssop-guide-agastache-foeniculum/ ) finally confirmed it for me with this statement:
Is Anise Hyssop the Same as Hyssop?
Anise Hyssop (Agastache) is not the same as Hyssop (Hyssopus). Anise Hyssop is Native to North America and a member of of the mint family, while Hyssop spp is a member of the carrot family and native to Europe. They are completely different genus and species!
But this page ( http://gardenersapprentice.com/gardeningtips/hyssop-and-agastache/ ) threw more mud in referring to the agastache as hyssop (maybe because it's considered a "common" name?) So did this site ( https://draxe.com/essential-oils/hyssop/ ).

So, fellow permies, who can clarify if there are major differences in the two species, if there are differing uses for the 2, or anything else I might want to know about what seems to be two separate species that have such intertwined and similar uses for pollinators, medicinal uses, and other uses I may not yet be aware of?

Next year, I'll be able to answer this question much better, as I now am only growing the hyssopus officinalis.  It's a much smaller plant that the big and beautiful anise hyssop that I am buying seeds to grow next year. But I can say that both of these plants are in the lamiaceae family, the family of mints, sages and deadnettles. Another name for hyssopus officinalis is hummingbird mint.  Carrots are in the umbelliferae family, like umbrella for how their flowers are formed.  Hummingbird mint has mint-like flowers, not carrot-like flowers.

I have not explored Anise Hyssop, but it does seem to be a very different plant.  Here is what I have learned about Hyssop.  https://southernappalachianherbs.blogspot.com/2021/08/hyssop-ancient-cure-all.html

Cindy Haskin wrote:.... hyssopus officianalis, which seems to be of the carrot family. Most websites have not been helpful in telling me that they are in fact different, though are used similarly if not identically. They both also seem to look very similar in their growth habits.

They are both in the Mint family, I can find actual medical information (as in chemicals contained) for Hyssop but not for anise hyssop that all seems to be folk medicine. The usage is very different and they do not appear to be suitable substitutes for eachother at all.

I grow and forage Agastache foeniculum because it's native to where I live. I mostly just eat it or dry it for tea (not necessarily for medicine but just as a beverage). I don't know how it compares with true hyssop, but here is a glimpse into traditional uses of anise hyssop:
http://naeb.brit.org/uses/search/?string=agastache+foeniculum

My wife asked me to grow hyssop. I didn't know there were two, so I ordered seeds and grew Hyssopus officinalis (the non native.) Then I found out this was the "wrong" hyssop. She wanted the native Agastache.
But here's the kicker... Out in the herb bed this weekend we found the native Agastache growing happily all on it's own right where we were going to plant it anyway!

Hyssop can be used as a tea, quite nice, and is also used in herbal blends for various dishes. Agastache has a different taste,  really nice and quite intense, good for teas and even sirups, a bit like mint, but has a very distinctive flavour, for mint lovers this might be something to try.

According to Wikipedia, they are both in the mint family though the point of origin is different.

Anise hyssop is in the same family as hyssop (the mint family Lamiaceae), but they are not closely related. Hyssop (Hyssopus) is a genus of about 10–12 species of herbaceous or semi-woody plants native from the east Mediterranean to central Asia

https://en.wikipedia.org/wiki/Agastache_foeniculum

Hyssopus officinalis or hyssop is a shrub in the Lamiaceae or mint family native to Southern Europe, the Middle East, and the region surrounding the Caspian Sea. Due to its purported properties as an antiseptic, cough reliever, and expectorant, it has been used in traditional herbal medicine.

https://en.wikipedia.org/wiki/Hyssopus_officinalis

I just picked up a Agastache foeniculum on my lunch hour.
Love that smell!
I'm hoping it self seeds and establishes itself.