The key word here is “branding.” This refers to the logo mark and overall presentation of a company, reflecting the quality of its materials, clothing design, and manufacturing; perhaps its target audience; plus what values the company extols (sustainability, equity, and so forth). This package of intangibles becomes attached to the logo, such that a customer who enters a clothing store will see the logo colors, the logo itself, perhaps even the design of the store, and have an overall, internal moment of grasping on a deep level the ethos of the company.
As noted above, a clothing brand includes the logo but does not stop there. It also includes all relevant signage, marketing collateral, floor appliques, clothing hang-tags, television advertising, paint colors on the walls in the store, and on an on.
But to get back to the hang-tags, these are essentially print business cards for the brand, just as much as an actual print business card would be.