Similar, but it's a civil suit.
Since Reddit is a non-party (they aren't the one being sued) there are many limitations. For example, you can usually use a subpoena to get an original document from a third party if you know the document already exists and have already seen it but need an original. There are many different rules and laws about what can be requested and what cannot. Generally you can't go on a "fishing expedition" with a non-party. In contrast for someone who is a party, if you can convince the judge that something smells fishy enough you're allowed to go fishing for documents in civil suits.
Ultimately all the different rules give broad discretion to the judge. The companies file a motion to compel turning over the documents, and the judge hears arguments with a 'more likely than not' standard, and the 'balance of harms' done in either direction. The judge also considers concepts like the likelihood of success, if there is the possibility of irreparable harm (like revealing trade secrets), if something is harmful to the status quo (like discovery would harm or help something else beyond the trial), and other factors. Judges also need to consider if there are other, better sources for the information. They look at the rights of individuals versus the rights of society as a whole, the harms and benefits to each, the costs and difficulties and burdens, and much more.
Judges balance all of it and try their best. So if they get a motion to compel discovery by a non-party, the civil violation is relatively minor but the document would cause people to lose jobs or close businesses, or if the consequences of the subpoena could cost millions of dollars for a violation that has a maximum penalty of thousands of dollars, the judge can deny the request.
Most likely it will be like the past cases. There is very little the studios can gain, the value is low but the potential damage is high, the person's ability to engage in anonymous speech can be seriously harmed. The past judgements showed the judge understood the extremely limited value; it puts a huge target on the individual and does great harm, but the only benefits to the studio is that it might give an address that might match a known infringer, but doesn't give any actual evidence of infringement, nor identity of a person who might have infringed. Huge harm for nearly no social benefit, the harms outweigh the benefit.