Sometimes the one/two letter designation is the branch/train/platform identifier.
Here is an old list of common branch identifiers:
M/T – 800 Series ISR, ISRg2 (1900, 2900, 3900), Connected Grid Router 2000
S – 7600 Series Router, ME 3600X, ME 3800X
GC – 5900 Series Embedded Router
SE – Catalyst 2960, 3560, 3750, IE 3000 Switches
SG – Catalyst 4500E (Sup 6E and earlier)
SY – Catalyst 6500E, 6807-XL, 6880
EA – IE 2000 Switches
Reference:
https://www.packetmischief.ca/2013/12/09/ios-and-nx-os-platform-identifiers/
As you already identified, "S" could also be a consolidated release. It is hard to say whether the "SE" is merely an identifier or whether it has deeper ties to the "E" releases.
"X" however in this case, most likely refers to an IOS "Special Release". This is supported by the "ED" designation that you have already identified as "Early Deployment".
X Special Releases are defined as:
Special Releases
Are similar to rebuilds but instead of quick fixes, special releases
introduce new features or additional platform support to quickly meet
market demands.
• A branch from a train code base.
• Does not conform
to a strict naming convention. They use a double letter after the
release number.
• The first letter could be a one-time release, the
train identifier, or the technology identifier.
• The second letter
could be a sequential revision or a one-time release.
• Special
releases do not have an EoL, they are integrated back into the parent
train.
This illustrates how Special Releases are integrated back into a parent train.

(Slides 15 and 18)
https://www.cisco.com/c/dam/en_us/training-events/le21/le34/downloads/689/academy/2005/BRK-101.pdf
The release notes from Cisco on IOS Release 15.0(2)EX call out the new features introduced in this special release.
What’s New in Cisco IOS Release 15.0(2)EX
First release of the Cisco Catalyst 2960-X Series Switches supporting
two different feature sets:
LAN Lite feature set—Provides standard
Layer 2 security, quality of service (QoS), and up to 1024 active
VLANs. LAN Lite models have reduced functionality and scalability with
entry level features in layer 2 and provide no routing capability.
They do not support stacking.
LAN Base feature set—In addition to the
LAN Lite feature set, the LAN Base feature set provides more advanced
Layer 2 features, extended scalability, routing capability, and
support for stacking with FlexStack-Plus.
https://www.cisco.com/c/en/us/td/docs/switches/lan/catalyst2960x/software/15-0_2_EX/release_notes/OL30810.html#pgfId-246822