1.)If you want to train for power/strength( is there a difference?)
Yes there is. There is limit strength, commonly referred to as plain out brute strength it's moving maximal weight possible, obviously you train using maximal weights at low reps. There is power, I would describle power as explosiveness, the ablity to make your muscles fire like an explosion. I have read some westside guys actually time their power (dynamic) training to get down to the shortest time periods possible to perform reps. Training is used with nonmaximal weights, 50% for example, the point is if you apply maximum momentum to 50% of your maximal training weight, the load will be much greater than just 50% of your maximal training weight due to the force you are applying.
2.)Is it okay to just lift fast??
Yeah that really depends on who you ask. There is a very recent t-nation article by Chad Waterbury discussing lifting speed. He is obviously against time under tension but give it a read if you want. Hope this answer doesn't come out bias. Might add, my opinion is it's best to lift fast but lower the weight controlled, controlled that is, no bouncing the bar off chest in bench press, no bouncing off the box in a box squat, etc. Control it.
http://www.t-nation.com/readTopic.do...itan?id=529331
3.)Or should you do exercises like jump squats or olympic lifts or pylometrics?
You can apply speed to any exercise you do, some are better than others although. Common ones are speed bench, speed deadlift, and speed squat. Jump squats are great, olympic lifts are great, etc. Ex:power cleans are great for developing power (explosiveness). They are an olympic movement. Yet you could do hang cleans and high pulls which directly correlate to the power clean. That's what makes it so fun.
4.)Also is it possible to gain muscle and power at the same time? if so, how?
Of course. If you are training intense whether it be for "hypertrophy" *record skip*, wait, I am waiting for direct training "to get bigger" to die out. Train for some athletic goals like the two you mentioned, limit strength and power for example (the westside template works well for both of these). You want to gain muscle? Ok, eat more quality food sources than you need for maintenance, done (that's drastically over simplifying, for more info about nutrition, check out the nutrition forums). The more I think about people lifting 3 sets of 10 reps on everything mindlessly I think to myself...god why?! It's like why don't you actually train to gain some real athleticism (did i spell that right?) instead of ballooned hypertrophied muscle tissue you aren't even utilizing, hell, you aren't even utilizing the muscle you have NOW. Not to say the 3 set 10 rep range doesnt have its place but when thats all you do year in and year out, come on now. "Don't cheat ya self, treat ya self."
There I took a stab at your questions, hopefully I shed some light.
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