different interpretations of two very close sentences

[vil]

Dear teachers,

Would you be kind enough to explain to us the difference in interpretation of the following two sentences?

I forgot to buy a newspaper.

I forgot about buying a newspaper.

V.

[leonardoatt]

1-You were supposed to buy a newspaper but you didn't because something might distracted your attention from buying that.
2-You exactly remembered to buy a newspaper but you didn't because you didn't want to.

[5jj]

I forgot to buy a newspaper.

I forgot about buying a newspaper.

V.

In practical terms, there could be no difference.

However, it is possible, in the right context, for the second to mean that you forgot buying the newspaper, i.e. you forgot that you had bought it. Although one interpretation is that you didn't buy it, and the other is that you did, context will make it clear which is intended.