Either is correct in a situation where changing from one to the other doesn't change the meaning of the sentence. This is usually determined by the verb we are using (and sometimes by the context in which it's used). If the verb always has the meaning of moving from outside to inside or vice versa, then changing the preposition doesn't affect the meaning. Otherwise it does. Compare these:
I put the meat on the grill.
I put the meat onto the grill.
I put the milk in the refrigerator.
I put the milk into the refrigerator.
In these cases, the meaning of what has been done is not changed at all. The meat wasn't on the grill, and once I put it there it was. The milk wasn't in the refrigerator until I put it there, and then it was. Now, have a look at these:
I told him not to run in the house.
I told him not to run into the house.
I walked in the mall.
I walked into the mall.
In these cases, the meanings are quite different. Running in the house means running while in the house, while running into the house means running from outside the house to inside the house. Similarly with the next pair, walking in the mall means walking around in the mall, whereas walking into the mall means walking from a point outside the mall to a point inside the mall.
Now, here's an example where context matters:
He fell in the bathtub.
He fell into the bathtub.
He fell in the well.
In the first sentence, he was in the bathtub when he fell. In the second, he wasn't in the bathtub until he fell into it. This is also true of the third case, but it's hard to think of a way that one could fall while already in the well, so in has the same meaning as into.
Typically, when changing the preposition doesn't change the meaning, we will use on or in rather than onto or into. This is not a hard-and-fast rule: "nail the picture onto the wall" seems more usual to me, and "insert the letter into the envelope" seems very much so. My feeling is that more formal verbs will tend to use into/onto in situations like these.
Finally, there are plenty of verbs that are a bit ambiguous as to whether they always imply movement between outside and inside, and spread is one of these. The peanut butter might already be on the bread before you spread it, and it might not be. Also, the peanut butter isn't on the part of the bread onto which you spread it before you do so, and then it is. But it's on the bread itself. So, you can look at it either way, and use either preposition.