We realized (last summer) the moths flying in our living area were pantry moths....a vigorous clean of our entire house led me to the discover holes in some garments -- and a vintage fur coat that had obviously been attacked. It has been in my freezer for a year now. Things returned this year...another major clean, but I am completely paranoid about the moths in my closets and unsure how to be sure we have gotten them. We have gotten rid of a large amount of clothing, cleaned and dry-cleaned, vacuumed and washed and most recently sprayed with Doctordoom (permethrin .50%) and let off a Knockout fumigator (Pyrethrin & piperonyl butoxide). All the clothes moths images I find are of a complete buff coloured insect....the ones I have caught in a clothes moth trap are approx. .5cm with a fawn coloured centre, and black or dark brown along the wings...one of the bugs had a tuft of reddish 'hair' on it's head.....the rest did not....on one (using a magnifying glass) I could see the long fringes at it's wing ends... my moths do not look like either the case making or the webbing moth and we have never been able to find any larvae or cocoons....ditto for my pantry moths...we have seen silky threads something keeps trying to make in my window casings...I once found a moth near it, and despite dusting with diatomaceous earth and a complete take-apart cleaning of all my windows, I saw a new one the other day. We live in the Pacific north west, which is prime spider territory....not sure if these 'webs' are related to my moths or a spider i haven't seen...I am currently paranoid to put anything back into my closets and I have been told the moths on my fur coat may not be killed by the deep freeze (it is a chest freezer) only slowed down....
First, I think you are confusing meal moths (pantry moths) with clothes moths, the two are not the same moth. You will almost never find clothes moths flying around the house as they tend to avoid light. Meal moths feed on dry foods like grains and dry pet food whereas clothes moths feed on animal fibres like hair and silk (see http://www.livingwithbugs.com/clothes_moth.html
for a comparison). The attached photo appears to be a casemaking clothes moth. The best option is cleaning and proper storage of CLEAN clothes, see the page cited above. The other photo looks like ordinary spider webs. Post a follow up if you have questions after looking over the pages cited above.
BTW, freezing will kill all stages of both moths.