They are not "vague" from the Japanese standpoint. Seen from the opposite side, I must say English is equally confusing. How do you distinguish 胃 and 腹 when they are both "stomach" in English? How do you distinguish 恋 and 愛 when both are "love" in English? How about 兄/弟 ("brother"), 胡椒/唐辛子 ("pepper"), ごはん/米/稲 ("rice"), 水/湯 ("water"), 絵/写真 ("picture"), 便所/風呂 ("bathroom"), and so on?
The Japanese language makes no distinction between "watch" and "clock" at a single-word level. Just as English speakers do not think "water" has two meanings, Japanese speakers do not think 時計 has two meanings. 普通の時計 is either "ordinary clock" or "ordinary watch". There are compounds like 腕時計 ("watch"), 置時計 ("table clock") and 壁掛け時計 ("wall clock") if you really need to distinguish the types of 時計, but you should not use them without a reason.
As for 腰, it refers to the lower back and the pelvic part of the body (see the picture here), so it's an equivalent of neither "waist" nor "back". We also have words like 背中, ウエスト and お尻. See also: How can I differentiate between feet and legs?