Climbing grade conversion is the approximate translation of a climb's difficulty between the world's different grading systems — such as YDS, French, UIAA, V-scale, and Font. Because each system developed separately, conversions are only ever approximate, but they let climbers compare routes and boulders across countries.
A project is a route or boulder at the edge of your ability that you work on over many attempts or sessions — rehearsing moves, refining beta, and building strength — until you can finally send it cleanly. 'Projecting' is the process of methodically piecing such a climb together.
To send a climb is to complete it cleanly from start to finish without falling or resting on the rope or gear. The word covers any successful clean ascent — an onsight, flash, or redpoint all count as sends. 'Sending' has become general climbing slang for nailing a goal.
The crux is the hardest move or section of a climb — the part most likely to stop you. A route's grade is largely set by its crux, and climbers focus their beta, strength, and mental preparation on getting through it. A climb can have one crux or several.
Beta is any information about how to climb a particular route or boulder problem — which holds to use, the sequence of moves, foot positions, rests, and clever tricks. Climbers share beta in person, in guidebooks, and in videos, and using it changes whether an ascent counts as an onsight, flash, or redpoint.
A flash is climbing a route or boulder problem cleanly on your first attempt, but with the benefit of beta gathered beforehand — watching someone climb it, getting hold descriptions, or studying video. It ranks just below an onsight, which allows no prior information at all.
An onsight is climbing a route cleanly from bottom to top on your very first attempt, with no prior practice, no beta, and no watching others on it. It's considered the purest and most prized ascent style, because you solve every move in real time without any foreknowledge.
A redpoint is a successful lead climb of a route from bottom to top without falling or resting on the rope, after having practiced it. It is the standard benchmark for 'sending' a hard route and contrasts with an onsight (no prior knowledge) and a flash (first try, but with beta).