If an academic researcher wants to ask research related question or to start a collaboration etc. with another academic researcher, it is usually a matter of a polite and specific email. I have seem such initiatives from academic researchers towards industrial researchers (e.g., a postdoc asking about technicalities of a paper written by a Google researcher directly to the Google researcher). Is such research correspondence, without any prior research contracts/agreements between the academic institution and industrial researcher's company, also common from the other way around (i.e., an industrial researcher initiating a correspondence to an academic researcher)? How about research correspondence between researchers in two different companies? I am thinking of transiting to industrial research from academia and genuinely curious about this.
Disclosure: I am a researcher working in industry.
I think that the rule of thumb is: make it as simple as is wise, but not simpler (paraphrasing Einstein).
Always make it clear who you are (name, company, etc), and what your intent is (e.g., better understanding of a paper, creating your own implementation of an algorithm in a scientific publication for research purposes only, developing a new product based on a scientific publication, writing a patent, etc).
Be open and honest (e.g., do not claim that you just want to understand something, when in reality you want to use it in the development of a product).
If you are asking about quite generic technicalities (e.g., something you might also publicly ask to a speaker in a conference), you might just drop an email and ask. As long as you do not disclose any confidential information, and you do not expect so from the researcher, you just can ask the question.
When you do need to disclose confidential information (e.g., specifics about a product your company is developing), you will need to sign an NDA (non-disclosure agreement).
Also be aware that if you are asking the academic researcher to do work for you beyond just answering an email, or provide you with something of value (e.g., working code belonging to a scientific publication) a monetary reimbursement is in place.
For the latter two items it is quite likely that you will need to involve other people within your company (the legal department, a budget holder, your boss, ...) before reaching out.
I don't think there is that much difference between academia and industry except that in industry you probably have to clear it with your boss and/or IP lawyers before you mail ideas out of the company. I have received "cold" contact emails from industry, sure, not that many I've been able to act on though. I think the problems are pretty much the same: how much time does someone have, do they even read their email or not, etc. You will get lots of variation both inside and outside of academia on this. If you have enough money to pay for a PhD student for at least a year, then you will probably have not too much trouble getting someone's attention in academia wherever you are coming from, if you've done enough work to be sure you're approaching the right person / someone actively researching the area you need.
The other easy way to get an academic to collaborate with industry is to hire them as a consultant. But again, it has to really be their area, and they have to have time available, so you need to do research. But if you get the wrong person, they may be able to suggest someone else or at least something to read (if the problem's already solved so no longer of academic interest.)