Three of the most popular ones are clever, bright and smart.
Cleverness is about tool manipulation. It's about having a library of information and methods at your disposal that you can call upon to attack a problem. It's about the toolset. "Clever" researchers tend to be great at solving well-known types of problems, or well-defined problems that are attackable with existing approaches. It's a matter of going through the toolset until you find something that works. Clever people tend to be good at technical subjects that involve absorbing a lot of jargon and detail. They're not always so good at solving or understanding problems that aren't well defined, or seeing the bigger picture, or starting with a blank page.
Brightness is about being able to appreciate larger patterns and relationships that don't necessarily conform to an existing approach or definition. Bright people tend not to be so dependent on clearly-defined goals or methodology, and can take a more "free-form" approach to work, where the project parameters and characteristics emerge as the project progresses.
A computer programmer needs to be clever, but a software designer needs to be bright.
"Clever vs. Bright" is like comparing soldier ants with butterflies. The soldier ant, working with other soldier ants, manages to overcome a lot of problems even if each individual ant doesn't really know where they fit into the larger scheme of things. The butterfly arguably has the better world-view, but can't always do very much with it.
Smartness is about being able to understand and exploit opportunities to gain advantage and achieve goals. It's possible to be clever and bright without being smart. Having "smarts" means that you learn from experience and think ahead strategically, to plan how the workings of a system can allow you to achieve your desired outcome.
Smart people are often also bright and clever, but they're also smart enough to realise that their success doesn't depend on cultivating those other skills to the same extent, because once they've become moderately successful, they can "hire in" clever and bright people to do that part of the work, and delegate. Successful entrepreneurs tend to be smart, and bright, and clever, but their focus is on being smart.
Military R+D usually wants researchers who are extremely clever, but not necessarily too bright or smart. A "bright" employee might query what their work is to be used for, notice how their research fits together with others to produce a device that they aren't supposed to know about, or query the legality or ethics or consequences of the project they're involved in. A smart researcher might realise that the market value of their work is more than their current employer is paying, leave to take a better job when they realise that the project is in trouble, or try to wrest control of the project from the existing managers.
Now, this is where it gets complicated:
People who describe themselves as smart (outside a limited peer group) usually aren't.
Smart people tend not to publicly identify themselves as as smart, because it's usually not a smart thing to do. Clever people sometimes describe themselves as smart, because nobody's actually told them what the words mean, and they're not bright enough to work it out for themselves. They follow the lead of the other clever people in their group that they've heard describing themselves as smart. The bright people also don't normally describe themselves as smart, because they only hear the word being used self-referentially by people with poor social skills who are "clever-only", and they decide that they don't want to be lumped in with them.
So if you're studying monkeys in a zoo that are picking grubs out of a log that have been put there by the zookeeper, the clever monkey will become adept at using a stick to extract the grubs, the bright monkey will watch the zookeeper and only go grub-hunting when the log's just been refilled, and the smart monkey will congratulate the other two on their cleverness, assume a management position and a share of the grubs, and then patent the stick.
Different skills.
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