Do 和 and 及 refer to two different kinds of "ands?" At one level, they both mean "and." At another level, 和 also means "peace," while 及 means "to extend." This suggests different usages.

Is one used to connect nouns, while the other is used to connect predicates, for example? And which one (both, or a third) would take the place of "and" in 和 "and" 及?
Both “和” and “及” are conjunctions for connecting two words or phrases.


和 [hé] : To connect nouns, verbs or phrases, not necessarily expressing a relationship and often informally. E.g. 汽车和现金 (car and cash),
蓝宝石和翡翠 (sapphire and jade).
及 [jí] : Mostly used in writing to connect nouns, with greater emphasis on the items preceding it. E.g. “囧”字的读音、意思及其常用表现手法


Example of combined usage adapted from Google's policy:


  我们的目标是不断超越，为您提供一流的服务和易于使用的安全及隐私权工具。


Note the order and how “和” is used to join the larger phrases together.

See also:
Difference between 与，和 and 跟?



There are a lot characters meaning "and": 和/及/与/而/又/并/同/亦/且/兼/跟"


  面包 和 黄油 bread and butter 
       一个女人﹑ 两个男人 及 三个孩子 one woman, two men and three children 
      《儿子 与 情人》 Sons and Lovers 
      缓慢 而 仔细地 slowly and carefully 
      能读 又 能写 able to read and write 
      他为她感到难过， 并 试图使她振作起来。 He was sorry for her and tried to cheer her up. 
      你 同 他一起去。You and he go together.
      他生 亦 穷来死 亦 穷。He was born poor and died poor. 
      一个优雅 且 和蔼的女人 a graceful and gentle woman 
      他担任教练 兼 队长。He doubled as coach and captain of the team. 
      你 跟 他一块儿来。You and he come togther. 


It is very hard to give specific rules on how to use them. You need to read a lot Chinese text to build up your language sense on those characters. But one rule seems holding the water all the time: if there are mutliple level things in the same sentence to be joined by "and", then you will need to use different characters.