1. I remember him playing the piano.

2. Their main job is protecting the President.

3. Appointing the committee proved surprisingly difficult.

4. They left the room complaining about the test.

5. My sister is studying classical Greek in Athens.

6. The teacher found his proposal appealing.

7. We saw John crossing the street alone.

The underlines in #1,2 and 3 are gerund and ones in #4,5,6 and 7 are present participle.

It's easy for me to distinguish everything except #1 and #7.

Do you know why #1 belongs to the gerund and #7 the present participle?
Hi,

I remember him playing the piano. (I remember the event of him playing the piano.)

We saw John crossing the street alone. (We saw the action: John was crossing the street alone.)
Hi,

1. I remember him playing the piano.

2. We saw John crossing the street alone.

Micauber said #1 can be said "I remember him when he was playing a piano"

Then I think #2 can be said "We saw John when he was crossing the street alone"

Up here, #1 and #2 are the same, I suppose.

But #1 and #2 may be different with this reason:

Perhaps #1 cannot be said "I remember him when he played a piano" because we can't say I remember him play the piano; but #2 can be said "We saw John when he crossed the street alone" because we can say We saw John cross the street alone.

Do you think my reason makes sense?