Learn English – better way to say “space for improvement”

The two sentences that you present are entirely synonymous. In this case, there is no difference in their meaning, both connotatively as well as denotatively.

As Damkerng said in the comments, the best option in my opinion (and the most common in my experience) is

We accept credit cards.

The fact that the credit cards are used for payment doesn't need to be stated - it is implied, because that is the only thing you can use credit cards for.

1. Read the following for more. This may mean read the following for more detailed explanation, or simply continue reading for more of the same: it may be a continuation of the story or discussion.

2. Refer to the following for more information. This means, if you want more details about what you have been reading, or more explanation that goes more in depth than the original text, read more here.

3. Further reading. This is the same as number two, just more professional.

The differences between these meanings are pretty subtle, and have a lot to do with tone. They also progress in formality, one being pretty casual, 3 being formal, and 2 somewhere in between.