How many types of mining pool are exist for bitcoin or litecoin?
The pools are mostly distinguished by:


fees: how much the pool charges workers
size: the larger the pool, the smaller the variance of your payouts
payout style: pay per share, pay per last N shares, etc.
location: do they have a server near you (extra latency will mean less mining work accepted and a lower payout)


As you guessed, getwork, long poll, stratum, etc. are not types of pools, but rather types of protocols for getting mining work from the pools. Some pools support more than one type of protocol.

You can see a nice comparison of various BTC mining pools here:
https://en.bitcoin.it/wiki/Comparison_of_mining_pools