Rigid
Part of speech: adjective
Definition: Stiff, rather than flexible. Fixed, rather than moving. Rigorous and unbending. Uncompromising.
Example sentence: And if you are playing in several meters at once, there has to be a - not a rigid - but there definitely has to be a reference to a common pulse in the band.
Strict
Part of speech: adjective
Definition: Strained; drawn close; tight; as, a strict embrace; a strict ligature.Tense; not relaxed; as, a strict fiber.Exact; accurate; precise; rigorously nice; as, to keep strict watch; to pay strict attention.Governed or governing by exact rules; observing exact rules; severe; rigorous; as, very strict in observing the Sabbath.Rigidly interpreted; exactly limited; confined; restricted; as, to understand words in a strict sense.Upright, or straight and narrow; — said of the shape of the plants or their flower clusters.Severe in discipline.
Example sentence: I'm actually no longer a strict vegan. I don't hang out in the cheese section - I don't even eat cheese. I don't drink milk. But every once in a while I'll have an egg. I'm going to eat eggs that come out of my next-door neighbor's farm, that's just the way it is.