The water's a bit muddy here
The errata (Chapter 8, "Combining Game Effects") you cited regarding the same-name rule goes on to explain what counts as a "feature".
Game features include spells, class features, feats, racial traits, monster abilities, and magic items.
As such the most potent feature would trump the other. Until either feature's effects run out of time, then the longer-lasting one is "reapplied", as per PHB (Page 205, "Combining Magical Effects"):
[...] lnstead, the most potent effect -such as the highest bonus-from those castings applies while their durations overlap.
The DMG-Errata shares the ruling of overlap. However, there is is some conflicting information between the PHB and the Errata:
Where the PHB says:
[...] the most potent effect -such as the highest bonus- [...]
The Errata states:
[...]only the effects of one of them—the most potent one—apply [...]
Given what you rule by, RAW without or RAW with Errata your criteria for what is done actually morphs drastically
What constitutes potency?
RAW by Errata, quantifying a feature's wholesale potency and nullify any misaligmed effects either version may not share with its name-twin is hard or in some cases perhaps even impossible if the features somehow have vastly different effects, but end up being equally "strong". How exactly you rule that is left wide open.
You have to house-rule that. Below you can find how I approach overlapping features.
RAW the DMG-Errata provides no criteria for what makes a feature more potent; however it does point you to what the PHB has to say about that.
RAW the PHB hints at how you can quantify the potency of a spell specifically, it does not use the word feature. If you go pure RAW this is where the trail ends. Reading it Rules As Intended I'd say a spell is a feature and no effect I know of is forcibly required to originate from a spell; so if you can quantify a spell by effect that should work for any feature.
Backed by the PHB's mention of effect-based potency, I compare each individual effect two features of the same name have and then pick the strongest for each. That also constitutes that the unique parts of one feature are compared against "nothing", meaning by virtue of existing they'd trump the lack of any counterpart in their twin.
Using your example:
The golem's ability is a monster ability "feature", the spell is a spell "feature". Since they both fit into that group and share the same name effects that "overlap" would be trumped by the most potent version. The target would also suffer the unique effects from the slow spell feature, i.e. the AC penalty, Dex disadvantage, etc.
And what about the save?
Now, thinking a bit further with regards to DC(s) the PHB's rule of using only the most potent version the DC of the stronger feature user would apply if we go by the definition of comparing each effect individually. So, the save from the amalgamated slow features would be 17 if the spell feature slow is cast by a creature with a spell-save below 17, and the other way around if the caster has a higher spell-save.
Saving whilst both (or more) features are in effect would then end all ongoing effects from both (or all) features of the same name. If one feature ends sooner than the other(s) the highest ongoing save takes hold until there is only one or no more feature.
Shouldn't I have to save from both (or all) features individually?
If you count the saving throw as an effect, no. If you see it as something else, maybe?
In a sense both slow features above offer the "effect" of the target being able to perform a save, the only thing that may differ is the number they have to hit.
What if I have one feature with variable effects? For example, would Blindness/Deafness cast twice blind and deafen a creature?
Blindness/Deafness lets the caster choose to inflict one of two effects, each targeting a sense of a creature.
If you follow the DMG-Errata's 'all or nothing' mindset for features the most potent feature-use of Blindness/Deafness would take hold, and if the "lesser" feature-use lasts longer it takes hold once the more potent feature runs out. Already that sounds and feels weird. Let's play out a quick scenario under the assumption that blindness trumps deafness.
Also assume that the target has terrible rolls has to endure the feature-uses to their fullest.
- The first cast successfully blinds a creature
- Half a minute into the fight you again cast successfully to deafen it, which does nothing, keeping the blindness as a superior
- Another thirty seconds later the first cast to blind runs out of time, creature's eyes clear up, it laughs hysterically then realises it's deaf for thirty seconds
Now, that scenario 'works' mechanically, but again; how do you define what feature-use is more potent?
Looking for any hints, RAW, there is nothing that would put hearing above seeing or vice-versa. This, again, calls for further house-ruling on these questions:
Is either sense objectively "superior"?
I'd say no, each race / creature has different foci for its senses (bats mostly rely on hearing, giraffes not so much).
Does a given spell (or [perhaps nonmagical] feature, in general) somehow "know" what would affect a given creature most?
Using Blindness/Deafness as an example again, the caster chooses the sense, the feature doesn't state anything like "on a fail the creature loses its most potent sense".
Using the method of 'comparing effects' individually I would follow this train of thought:
Blindness and deafness target a creature's senses, they have that in common
A creature's vision and hearing are specified as different targets
Each effect works on a different aspect of the target creature
Blindness trumps nothing, Deafness trumps nothing
If both saves fail, both effects take hold.
And the DC?
Same as above. Same name, same bane.