Red comes in many varieties and some of those might make you look radiant, healthy and vibrant, whereas others won't do anything for you or could even make you look tired, blotchy, unwell, or older than you really are.
This has to do with the combination of your own colors (hair, eyes, skin tone and skin undertone) with the particular type of red that you are wearing. This is especially so if you are wearing the color close to your face.
Overall, the chroma (vividness or brightness), the temperature (warm -leaning orange-yellow or cool -leaning purple-blue) and resonance (tinted, shaded, toned, washed, blended) have to match with or complement your particular red as it shows up in your skin tone or hair (no matter how subtle --- some of us show very little red on the surface).
Let's dive in and look at some reds
Coral Red is a warmer type of red temperature wise. It's chroma is medium as it is slightly toned. An excellent color for the warmer seasons like Spring and Autumn, although some very bright springs should opt for a more vivid red, such as vermillion.
Burgundy or sometimes called 'bordeaux' is one of the coolest (leaning more towards purple-blue) and deepest (toned or shaded) reds, named after the wines from the region of Bourgogne. A color very well suited for the softer summers as well as some deep winters. For Autumns this is too cool, they would look for Maroon instead.
Ruby red is as cool as as Burgundy, but it is brighter than burgundy and has more chroma. The cooler Winter types as well as the cooler (and brighter) Summers wear this very well.
Vermillion is bright, just like ruby, however, the temperature is much warmer. A color suited for the bright spring.