In general, ''peak" is used more in the sense of "pico, topo, ponta", that doesn´t mean that it sometimes can´t be used in the meaning of "níveis históricos" (Dollar rise, for example...or a activity peaks of some kind of pandemic virus etc.)
Spike suggests "um pico de..." (prices, activity, current, etc) that is a "burst" of sorts happening.
It can also suggest some kind of "ponta" (a spiked gate/fence)http://thumbs.dreamstime.com/x/spiked-fence-3154334.jpghttp://i.ytimg.com/vi/7YwQbTBCBKs/hqdefault.jpghttp://www.gwoltal.myfastmail.com/files/Spiked%20Hairhttp://www2.pictures.stylebistro.com/gi ... c4_YKx.jpg
And sometimes they mean one and the same thing.
To get used to both word senses, look up the words in a good dictionary, Linguee, word sentence sites, etc.