Exactly.
Diesel-mechanical (engine-gearbox) is classes 10x/11x/12x and [14x as built] for the old SCG 4-speed box, then 172, NI C4K and 195/196/197 (edit - and MPV) use a modern ZF 6-speed box.
Diesel-hydraulic (engine-hydraulic transmission) is classes [14x re-engineered], 150, 153, 155, 156, 158, 159, 165, 166, 168, 170, 171, 175 and NI C3K for the 2-speed Voith hydraulic, and 180 and 185 for the 3-speed Voith hydraulic. Was unusually also used by locomotives of classes 35, 41/42/43 (Warship) and 52.
Diesel-electric (engine-generator-traction motors) is classes 20x and then 220, 221, 222, 230 (London Northwestern, as was) and 231. Also used by the vast majority of diesel locomotives (including the HST power cars), the "diesel mode" of bi/tri-mode locomotives, and the "diesel mode" of bi/tri-mode units (230 Transport for Wales, 755, 756, 769, 800, [801 "rescue engine"], 802, 805 and 810 - edit - and 820 and 897).
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The acronyms for all three types are:
DMMU - Diesel-Mechanical Multiple Unit
DHMU - Diesel-Hydraulic Multiple Unit
DEMU - Diesel-Electric Multiple Unit
and then DMU (Diesel Multiple Unit) includes all three.
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Sometimes though, you'll hear/see (as indeed you did) DMU ("diesel") and DEMU ("diesel-electric").
In this case, DMU is [DMMU and/or DHMU] and DEMU is, well, DEMU.
This latter way does align with the TOPS class number ranges, as [DMMU and DHMU] ("DMU") are 1xx, then DEMU is 2xx.