Seamed Cups versus Foam-Moulded
Besides underwired/ wire-free, the biggest division in bra styles is probably foam molded versus seamed. As expected, both bra types have advantages and disadvantages.
Molded cups, or "T-shirt bras," are smooth under clothing and are made of a thicker material that provides more nipple coverage. (This bra category is also sometimes called "padded bras," but that doesn't mean *extra* padding necessarily.) Their shape is very specific, though, and depending on the structure and firmness of the cups, the fit on your individual curves may be hit-or-miss. If you strongly prefer this bra type, expect that you may have to try several different styles to find one that is a good match for your body shape. Due to structural and fabrication issues, molded cup bra sizes also don't go as large as seamed styles.
Bras with seamed cups, also called multi-part or cut-and-sewn styles, provide better support in larger sizes and are more varied in terms of aesthetics and design. Their thinner material doesn't provide the same level of coverage but does a much better job of conforming to your shape for an easier, flattering fit. Though seam contours may be visible through some clothing, how much they show will depend on the seam placement, bra material, your body shape, and what sort of top you're wearing.
If you've only ever worn molded cup bras, consider trying on a seamed bra for comparison. You may find that you like the fit and fashion more than you'd expect.
Pictured: First image- Elise by Fit Fully Yours, Aline by Parfait, and Virginia by Corin; Second image- Minx by Skarlett Blue, Illusion by Fantasie, and Serena by Fit Fully Yours