It’s not difficult to separate these two words. Everyone knows the affectionate embrace of hugging someone. The word possibly comes from an Old Norse word, hugga, meaning to soothe or console. Clinch suggests tightly holding someone for other purposes—usually to prevent them from moving. Boxers clinch their opponents by putting their arms around the opponent’s body and arms, and leaning on them to prevent punches or to gain time until one of them manages to break out of the hold. This verb is usually used intransitively: Sugar Ray Robinson and his opponent clinched. The more frequent use of clinch is as a verb meaning to secure a deal, title, or victory—that is, to make sure it’s not going anywhere.
Both words refer to growing or becoming greater. To increase is to grow in number, size, strength, or quality. It implies the simple fact of something becoming greater as opposed to shrinking or staying the same: The population increased by 2 percent. Escalate, which derives from escalator, an invention in use by the 1920s, suggests a steeper, sometimes alarming increase in intensity or magnitude, sometimes in prices, but more often in tense situations. If a situation, confrontation, or conflict escalates, it begins to get out of hand or threatens to escalate into something full-blown.
Climb covers all means of physically going up or reaching the top of something using one’s hands or feet or both—climbing a rope, a mountain, or the stairs. Clamber suggests a difficult or awkward climb that requires the use of both hands and feet: clambered up the rockface, the ladder, or aboard the ship. In actual usage, clamber is sometimes used for a more crawl-like action: clambered along a 40-foot log; clambering among the ruins. And to say that climbing plants clamber up walls (using their tendrils) is also an acceptable use.