Cattle are often interchangeable. You cull any that catch a disease (in some cases the USDA will cull the entire herd if just one catches something - bio security is a big deal) In the case of drought you pick a bunch to get rid of - based on market prices (If everyone else is you will try to keep yours because the market is collapsing - but this means managing feed and thus may mean culling more of the herd latter.)
Some cattle we can measure. Milk cows are carefully managed as to output - the farmer knows how much the milk each one is worth and so they can cull the low producers. However milk is so much more valuable than meat that they never cull based on drought - milk can always outbid meat for feed. If milk demand goes down the farmer might cull come - but often the farmer is under contract for X amount of milk and so they cannot manage prices.
But if you are milking you don't have bulls. Maybe you have one (though almost everyone uses artificial insemination these days). Worrying about milking bulls is like worrying about the NetWare server - once common but has been obsolete since before many reading this were even born.
Of course the pigs, cows, and chickens are not interchangeable. Nor are corn, hay, soybeans.
I think it's a way of thinking about things, rather than a true/false description. e.g. VMware virtual hosts make good cattle - in some setups I have worked on the hosts are interchangeable, move virtual machines between them without downtime. In others the hosts have different storage access, different connectivity and it matters which combination of hosts are online/offline together, and which VMs need the special connectivity.
The regular setups are easier to understand, nicer to work on. The irregular ones are a trip hazard, they need careful setup, more careful maintenance, more detailed documentation, more aware monitoring. But there's probably ways they could be made regular, if the unique connectivity was moved out to a separate 'module' e.g. at the switch layer, or if the storage had been planned differently, sometimes with more cost, sometimes just with different design up-front.
Along these lines, yes DNS is not NTP but you could have a 'cattle' template Linux server which can run your DNS or NTP or SMTP relay which can be script deployed, and then standard DNS/NTP/SMTP containers deployed on top. Or you could build a new Linux server by hand and deploy a new service layer by hand, every time, each one slightly different depending how rushed you are and what verison of installers are conveniently available and whether the same person does the work following the latest runbook or an outdated one or going from memory. You could deploy a template OpnSense VM which can front DNS or NTP or SMTP instead of having to manually login to a GUI firewall interface and add rules for the new service by hand.
'Cattle not pets' is a call to standardise, regularise, modularize, template, script, automate; to move towards those ways of doing things. Servers are now software which can be copypasted in a way they weren't 10-30 years ago, at least in my non-FAANG world. To me it doesn't mean every server has to mean nothing to you, or every server is interchangeable, it means consider if thinking that wasy can help.
It might have been the original idea (though taken into account the time period and context, I suspect we're missing possible overfocus on deployment by AWS ASG and smallish set of services).
What grinds my gears is that over years I found it a thought limiting meme - it effectively swings a metaphor too hard into one direction, and some early responses under original article IMO present quite well the issue. It's not like people are stupid - but metaphors like this exist to make shortcuts for thinking and discussion, and for last few years I've seen that it short-circuits the discussion too hard, making people either stop thinking about certain interdependencies, or stopping noticing that there are still systems they treat like "pets", just named differently and in different scope, but now mentally pushing out how fragile they can be.
Some cattle we can measure. Milk cows are carefully managed as to output - the farmer knows how much the milk each one is worth and so they can cull the low producers. However milk is so much more valuable than meat that they never cull based on drought - milk can always outbid meat for feed. If milk demand goes down the farmer might cull come - but often the farmer is under contract for X amount of milk and so they cannot manage prices.