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Time Machine weirdness

A Macbook Pro was running short of diskspace today so I decided to upgrade the drive to a larger capacity.

1) Turned Time Machine off (backup drive is a 1TB external dedicated to TM and with 40% free)
2) Made a bootable clone of the internal drive to a new 2.5" drive. The new drive is named "Macintosh HD" .... which is the same as the old drive
3) Pulled the small/full drive out of the Macbook and installed the new larger capacity drive.
4) Restarted the machine with the new larger internal drive
5) Turned Time Machine back on.

Time Machine now complains that there isn't enough space left on the external TM drive to complete a backup.

Is this:
a) a case where a clone drive isn't identical as far as Time Machine is concerned even though it is a bit-for-bit copy? ie. does TM use drive serial numbers or some other identifier to determine which volume to backup?
or
b) some other TM weirdness?

I'm pretty sure each drive is identified by its SN or some other identifier.

Easiest way to delete the old TM backup and start a new backup. make sure you dont erase the old drive until the backup is finished.
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The problem is that when you created the clone the new files are just that. New files. Time machine sees them as needing a backup. TM doesn't keep track of the hard drive in anyway. Different backups are tracked by computer name and the Mac address of en0. If you restore from the backup it shouldn't require another full backup.