Is there any kind of character customization like shaders or vanity slots to stand out from people using the same gear? How much can you tweak your "look?"
Each frame has five different regions you can color by hand, there are custom skins, and skins that are more than just skins (as in different geometry for armor and helmets), Syndanas which are things like capes and other accessories, special armor attachments you can use on the chest, as well as individually on each arm and leg. You can also apply custom animations (each warframe comes with three animation sets, but you can also spend platinum to use any warframe's animations on any other warframe). Besides that you can choose whether to show holstered weapons or not, per weapon, as well as buy different holster positions (ie. sword across back, or sword on the hip etc.), and weapons have their own skins, cosmetic attachments and editable color schemes as well.
You also get three different saved loadouts for your visual customizations for each frame.
Most of these options cost platinum, but sometimes there are special timed missions (Alerts) that offer helmet variants and weapon skins as rewards.
Fashion frame is a very real thing, and I'm sure DE is making a killing on all the options they provide. DE puts out special skin variants on a regular basis, but they also have a system called Tennogen where non-DE artists can make their own skins and get a cut of the proceeds from selling them in the Warframe store. There are a ton of amazing creations in Tennogen, and thats been the biggest platinum sink for me.
And that's not even going into the cosmetic customizations for pets, sentinels, your ship, your operator, your archwing, and your clan dojo. The way you create your clan dojo (hallway by hallway, room by room) and all the customization options there is one hell of a rabbit hole all of its own.