Re: What is the difference between a whammy pedal, octave pedal and tremolo?
Ace got it.
Great example of tremelo is on a song called "Never My Love" by a '60s band, The Association.
Leo Fender really messed things up by getting tremelo and vibrato backwards on his products. The VIBRATO in his amps is actually a tremelo circuit. The "Synchronized Tremelo" on his Strat is actually a vibrato that changes the pitch of the note.
The old "tuck and roll" Kustom amps of the '60s had a true VIBRATO circuit, adding a touch of pitch-shifting waver. Check out John Fogerty and Creedence Clearwater Revival. Boss has a new pedal that does this effect. Compare it to their TREMELO pedal.
The Digitech whammy does exactly what Ace described. It can do the deep "dive bombs" of the Floyd Rose Vibrato.
Take a look at the Boss line of effects. I had an older Boss Octaver pedal, and it would add a note one or two octaves below the fundamental note. I would occasionally use it with my guitar to reproduce a bass riff. Adds a lot of thickness, but you will want an amp and cab that can handle all that low-end. Wouldn't want to use for a gig to replace a bass player. Can be a little "synth-y".
One that I have on my pedalboard now is the Boss Pitch Shifter/Harmonizer. I use mine for two songs where I want to simulate a twin-guitar harmony lead. People ALWAYS ask me how I did that!

You MUST set the key of the song. Then, select the harmony...2nd, 3rd, 4th, etc., above or below, and then adjust the blend of the fundamental to the harmony note. You can also do octave up or down. I am currently working on a song to use this feature. Mine lives in my Mesas' efx loops, before the delays. Can be glitchy; you MUST play precisely--single notes. Can be a little "synth-y".
Some fuzz pedals have an octave up feature. Then there is the MXR Blue Box...what goes in may or may not be what comes out, lol! Check out ring modulators if you like mayhem. And there are other fun pedals like E-H POG, etc. The E-H "9" pedals can create keyboard tones. And the Roland/Boss VG-88 that can turn your Strat guitar into a Rickenbacker 12-string and your Fender Deluxe Reverb into a VOX AC-30! Oh the insanity!!!!
Look at some of the Boss videos, and you can get a good idea of what the Vibrato, Tremolo, Octaver and Pitch Shifter can do.
Good luck!
Bill