Learn English – Fair and Reasonable: Is there a difference

In engineering mechanics a rigid body will undergo no deformation whatsoever under any amount of force.

In contrast, stiffness is a measure of how much force it takes to deform a body by a given amount.

In general terms something is said to be stiff when it has a high stiffness coefficient, i.e., it takes a lot of force to deform it; but notice that it does deform.

As the stiffness goes to infinity the body becomes rigid, i.e., no amount of force will be able to deform it.

In practice, nothing is truly rigid, but many times assuming a rigid body simplifies the math needed to analyze a system and when the stiffness of the body is high enough the effects of the assumption are negligible.

Therefore in practice, I reserve the use of the word rigid for cases where there is no possibility for bending (whether figuratively, or literally) and use the word stiff when I believe bending is possible, albeit only with a large amount of force.

As for opposites:

opposite of rigid - deformable : able to be deformed

opposite of stiff - flaccid : not firm or stiff

Briefly, a festival is a gathering of people to celebrate something, historically religious holidays (feast days), but now also secular ones, e.g. Kwanzaa, or the Burning Man, initially held to celebrate the summer solstice. Mardi Gras is a famous New Orleans festival, a religious one celebrated more quietly in other areas.

A fair is a gathering of vendors or tradespeople for the entertainment and/or commerce/other purpose). There are job fairs (hardly a festival), book fairs, farm shows (also called fairs) where people show their prized livestock or farm products for the entertainment (and often sales for charity) of both fellow farmers and non-farmers alike, county fairs (mostly just summer entertainment), etc.