The two websites I listed provide different approaches to it. With nice hash, you simply choose an amount of power you wish to rent, and provide a price at which you wish to rent it. If any hardware out there matches your specifications, it starts working for you until all of your funds are used up, or somebody outbids you. With mining rig rentals, you choose one or more rigs and pay the rig owner a pre-determined rate for a specified time. During that time, it is as though those rigs are your own. You can point them to whatever pools you want.
Thank you Jonny for the detailed reply, I just realized that I had not phrased by question properly, I knew about the rental services I use them as frequently as my wallet permits. However I just wanted to understand if there is any co-relation between the time at which the rentals are put into the run, for example I saw a couple of posts which said "we are due a block" so is it with reference to a particular time at which putting in a rental increases the odds of finding a block?
I am sorry if I sound naive, pretty new to the mining arena, just been mining for a month now so totally new to this.
Thanks for your time though.