Packing machine or packaging machine

I have learnt that "pack" is the verb and "packaging" the noun (for the wrapping). Therefore I think the correct word must be "packing machine" for a machine which packs the product into "packaging" (for example a bagging machine). However in my work I see the word "packaging machine" very often, and this confuses me (English is not my native language).

Originally package was the noun from the verb pack but these days both can be used as both noun and verb. There are clearly some situations where either can be used, but there are definitely some differences and some situations where one is much better that the other:

• Pack is more common in the UK. Sometimes a different word is used in the US. For example, a pack of cards in the UK is a deck of cards in the US.
• Package is more common in the US. A package in the US often corresponds to a parcel in the UK.
• A pack often has a sense of completeness. So you can have a pack of cards - meaning a complete set you could play a game with. Things are often sold as a pack, meaning all the equipment you need for a given task, e.g. starter pack (everything you need to get started), a writing pack (all the equipment you need to write letters) and so on.
• When used as a verb, package comes from the noun, so you cannot package things in any other container. You cannot package clothes in a suitcase, or articles in a carton. If you package things then they end up in a package, by definition.

But things are also changing. In the past I (in the UK) would have got a parcel through the post, but these days I get a package from Amazon. This is no doubt because Amazon (an American company) uses this word.

packaging machines, according to Wikipedia, is an umbrella term used to define machineries that:

[...] complete stages of the packaging process. Examples include filling machines, sealing machines, wrapping machines, strapping machines, labelling machines and coding machines.

While packing machine is defined as, according to this patent:

A MACHINE FOR PACKING ARTICLES INTO CARTONS OF DIFFERENT SIZES [...]

In short, packaging machines include many machines that are used to package products. One of the many packaging machines is the packing machine -- a machine that packs items into containers.