Could you tell me please if the following sentences mean the same thing, or they have some difference?
After breakfast we went sightseeing/swimming.
After breakfast we went to sightsee/to swim.
After breakfast we went for sightseeng/swimming.
I wonder how to explain using the phrase "went sightseeing/swimming". Did it really come from the sense "went in order to sightsee/swim", or what is the same,"went for sightseeing"?
Or "swimming" is a direct object of "went" the way as "the distance" and "the lesson" in "we went the distance, we went the lesson, we went five miles". I hope you get what I mean. I really don't know how to get the gerund after the verb "go". Is it the shortened version of "went for sightseeing" or maybe, "went with the purpose of sightseeing" OR it is just "the direct object", like five miles in "went five miles" or "crying" in "to start crying" ?