Why do different manufacturers have different S.M.A.R.T value?

Okay, first of all I disagree with your premise.

Google did a study that indicates that certain raw data attributes that the S.M.A.R.T status of hard drives reports can have a strong correlation with the future failure of the drive.

In fact they found the opposite:

...we find that failure prediction models based on SMART parameters alone are likely to be severely limited in their prediction accuracy, given that a large fraction of our failed drives have shown no SMART error signals whatsoever.

Secondly, SMART thresholds are not standardised. The firmware on the drive itself will flag an attribute as being "pre-failure", but the raw values are meaningless to the user. For example, Seagate says:

Various attributes are being monitored and measured against certain threshold limits. If any one attribute exceeds a threshold then a general SMART Status test will change from Pass to Fail.

The SMART values that might be read out by third-party SMART software are not based on how the values may be used within the Seagate hard drives. Seagate does not provide support for software programs that claim to read individual SMART attributes and thresholds. There may be some historical correctness on older drives, but new drives, no doubt, will have incorporated newer solutions, attributes and thresholds.

tl;dr Summary:

Raw SMART values are almost meaningless, as different manufacturers use them in different ways and have different thresholds etc. The drive firmware itself will tell you when it is in "pre-failure"... or it might not, SMART really isn't very reliable.

Do regular backups!

It does appear that different manufacturers use SMART values for sometimes radically different things, as you can see here:

My hard disk(s) in ReadyNAS is reporting high SMART Raw Read Error Rate, Seek Error Rate, and Hardware ECC Recovered. What should I do?

Seagate uses these SMART fields for internal counts, so this is a known issue with Seagate disks. Look for abnormal counts in other fields, especially Reallocated Sector Ct and ATA Error Count.

So when it comes to your actual question ...

If I am lucky enough for a bad drive to show a hint of failure such as scan errors or reallocated sectors, I know to get the drive the heck out of there. If no such hint exists, I'll probably spend many hours troubleshooting slowness and data corruption until I finally find that the hard drive is bad.

I'd say a good rule of thumb is, you can only expect SMART settings to be comparable within the same drive manufacturer, and maybe even the same drive model!

So when you're looking at diagnosing those SMART counts, keep that in mind... one manufacturer's "read error retry count" may mean something totally different than another manufacturer's. Sad but true. :(

I'm not exactly sure what the question is that you're asking. You seem to have the whole question and answer rolled up into one but...

Have you compared the hard drive metrics to those given from SeaTools

It's Seagate's standard hardware diagnostic tool and AFAIK the most commonly used HDD diagnostic tool.

Don't be surprised if you find that the tools report unfavourable results about their competitors. The tools generally work with HDDs of all manufacturers but that doesn't mean that they have make their competitors look good while doing.

Haven't you ever heard the joke, "99.99% of all statistics are true except, of course, this statistic".