Love corsets? Prefer basques? Don't actually know what the difference is, you just know you don't own any?
I'm going to talk you through the differences (and provide you with some lovely links if you're inspired to shop). I should say, this is very much from a boudoir portrait session perspective - I'm not going to be talking about the benefits or otherwise of waist training here, as that's not a subject I know anything about. If that's what you're looking for, may I suggest going here.

Corsets

Corsets, more often than not, don't have straps (there will always be exceptions). They do have amazing boning to cinch in your waist and give you that "I'm not quite sure I can breathe" feeling. However, all boning is not created equally - there's acrylic boning which is more common in fashion corsets, and then there's steel boning. Steel boning is more likely to have a larger 'waist reducing' effect.
Whilst they're busy reducing your waist, corsets also push up the bust. This may sound like a fabulous effect, and it can look amazing. However, there is such a thing as 'too much of a good thing' and so for chests that are larger anyway, it's best to try on different corset styles - a sweetheart neckline might be more flattering than one that goes straight across, for example.

For my own portrait session, I wore a couple of different fashion corsets - they definitely had a waist cinching effect, which was good enough as far as I was concerned.

There's a massive array of corsets out there, in a whole host of different styles, from steampunk to burlesque to bridal. They'll usually have the option of wearing with or without suspender straps, and there are corset dresses  short (think Black Swan) . Many corsets are designed much more to be worn as outerwear than for covering up.

Underbust corsets are all about creating that cinched-in waist look (and are also more comfortable to sit down in).

I know very few people who can lace themselves into a corset (there's always someone on hand here to help you) - although I have watched a Youtube video and had a go myself. It was possible, but I suspect an extra pair of hands could have pulled it tighter.
 Corsets lace down the back, and should have puller loops half way down - so double check they're laced properly, before you start.

Basques

Unless you happen to be really brave, basques are much more firmly 'underwear' than corsets. The biggest difference is the boning - in short, a basque doesn't have any. They are usually structured enough to create a smooth outline for your body, but they're not really going to change your shape, if that's what you're after.
Basques are more likely to have straps, and, helpfully, cups. If you don't think that's much of a difference - try on a corset and a basque, lie down in each, and see what happens to your chest. Chances are, in a basque with cups your chest is going to stay pretty much in place. Should you happen to lean towards the 'breasts straying alarmingly towards armpits' look when you lie down without support, a corset is less likely to keep everything in place for you. That's a big difference!

Just like with corsets, basques may come with suspender straps, and often these will be removable.
Whilst I found lots of websites dedicated to corsets, there are less basques around - nonetheless, there are some gorgeous ones. Certainly, again, in the bridal lingerie world.

They're often designed to create the illusion of waist cinching, even if they're not actually doing the job. This does of course mean they tend to be much more comfortable to wear than corsets, although you may still need help getting in (and out) of a basque.

So which is best?

Whichever suits you and you feel the most comfortable in. You need to bring along a variety of outfits for a boudoir portrait session anyway (a minimum of 3), so you'll always have outfits that will work in different poses. It much more comes down to whether you're craving that corset 'look', in which case a basque is not going to deliver for you.
Much love,
Anna
xx