Is all #1 PET & #2 HDPE plastic the same?

I live in a city that will ONLY take #1 & #2 plastics for recycling when the item has a "threaded neck". Now I'm not a chemist, but I thought that if an item is stamped as a #2 HDPE plastic that it is chemically the same as any item stamped with the same, #2 HDPE. The exact written requirements state.. "HDPE #2 or PET #1 stamped on bottom. Only bottles or jugs with threaded neck. HDPE #2 must have a seam on the bottom and sides. Clear and green PET #1 containers only. Rinse clean....etc, etc." I have never heard of such stringent requirements and I'm baffled as to why so many #1 & #2 plastic food containers are left behind in my recycling bin. It's almost the city doesn't even want to be bothered with recycling anything. I've written the city's department for recycling twice and never get an answer, almost like they don't even know why. I'm beginning to think they originally made up these guidelines when they first started recycling 20 years ago because bottles and jugs were basically the only thing made of recyclable plastics back then and after many years of just re-issuing the requirements don't realize they need to re-evaluate their recycling program. :(