Quick Questions: Suggest

Can you tell the difference between these two sentences (aside from the fact that one speaks about drinking coffee and the other about visiting a doctor?)

He suggested going for a coffee.

&

He suggested that I should go and see a doctor.

 

suggest doing something: This form tends to be used when the subject of suggest is also involved in the activity.
e.g. He suggested going for a coffee = he is going for a coffee with the others.
suggest (that) someone (should) do something: This form tends to be used when the subject of suggest is making the suggestion to someone else.
e.g. They suggested that I should go and see a doctor.

However, it can also be used when the person making the suggestion is also going to be involved in the activity
e.g. He suggested that we should all go and get a coffee.