From good ol' dictionary.com, intercede means:
- to act or interpose in behalf of someone in difficulty or trouble, as by pleading or petition: to intercede with the governor for a condemned man.
Using this general definition, we can come up with one that applies intercessory prayer. Simply put, it's "someone praying on our behalf when we're in time of need".
Humans as our intercessor
Jesus is said not only to be our intercessor, but also our mediator
1 Tim 2:5 (NIV)
For there is one God and one mediator between God and mankind, the man Christ Jesus
Is this to say that others cannot intercede for us? Certainly not! However, if they pray to God on our behalf, they're actually using Jesus, our mediator to get to God.
Jesus, per this passage, is the one who talks to God on our behalf. Because of that, any human prayer will go through Jesus to get to God.
Jesus as our intercessor
Because of this, when Jesus prays on our behalf, it is going directly to God. When we humans intercede, it goes directly to Jesus and then to God. Clearly, this is one-step of removal.
But can we say, then, that our prayers sometimes do not reach God, when Jesus prayers do? I don't think we can go that far. However, I do believe that Jesus, being the direct contact with God, knows how to intercede far better than we do. (Granted, that's part of why we've been given the Holy Spirit.)
Holy Spirit as our intercessor
Romans 8:26 (NIV)
In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us through wordless groans.
This shows that the Holy Spirit is also interceding on our behalf, giving us the words to speak and praying for us when we don't know what to say.
Up until now, that covers all Christianity. All Christians believe (or should believe) in the above. Humans, Jesus, and the Holy Spirit intercede for us--pray on our behalf--to God.
Catholicism has taken this one step further, claiming not only that living humans can pray for us, but also that saints can pray for us.
The idea is exactly like asking for prayers from family members. You go to your family and say "Please pray for me in this issue" and they will intercede on your behalf, praying to God through Jesus.
Catholics believe (along with many other groups/denominations/sects) that saints in heaven can hear our prayers here on earth. Therefore, since they can hear our prayers, they can intercede for us in our need.
The argument behind that is an entirely different question.
Is there any one type of interceding that is better than another? Personally, I can't find any source saying anything like this. I believe that the more people you have interceding for a particular issue, the better.
However, it must be noted that all prayers from humans must go through Jesus, our one and only mediator. Whether those prayers are from Aunt Claud or Mary, mother of Jesus. All these prayers from humans go through Jesus or (in our own grumblings when we don't know what to say) through the Holy Spirit.
So, I couldn't make any solid, realistic arguments that one type of intercession is better than another.
Also, those listed above are the only "types" of intercession that I've been able to find. There might be other "types", but this is all I could find (or all that I know about).