Astringents vs. anti-inflammatories
There's a difference.
Astringents are topically anti-inflammatory, but anti-inflammatories aren't usually astringent.
An astringent is a local anti-inflammatory. You can use astringents for all inflammations of the skin - topically. You can also use astringents for all inflammations in the mouth and through the whole digestive tract: they act locally, they can't get beyond the mucous membranes or skin. They are anti-inflammatory because they tan both skin and mucous membranes; they dry them up, leaving no growing space for possible unfriendly neighborhood microbes. They'll also shrink any inflamed tissues, because as tanning agents, they remove moisture from tissues. Astringents are very straightforward.
An anti-inflammatory works systemically, in the whole body. If you drink a tea of an astringent you can't ever expect it to work on, say, a bladder infection or a cough. If you drink a tea of an anti-inflammatory you can expect it to work as an anti-inflammatory throughout the body.
There are of course herbs which are specifics for different places in the body. But if you have a cough, but don't have any of the cough herbs, a general anti-inflammatory will help you some, too.