A combi is a heating and hot water system all in one box with no
external Tanks or cylinders. Hence the name "combi" from
combination.

Yes, but the term does now seem to mean an instantaneously heated system,
rather than a storage based one. However, it is only a name and I see no
reason to argue over that. The important thing is matching the performance
of the system to the expectations of the user.

Some are, some have an integral unvented cylinder inside the box too.
The ECO-Hometec gives a flowrate of 22 litre/minute, which is
infinitely continuous, if that is what you mistakenly mean by a
"proper combi".

22 lpm is too slow for me. I'd rather lose the infinitely continuous and
gain immediate gratification at the expense of a little loft space. However,
22 lpm would run a pretty excellent shower, or two good ones, so could be
very useful for a household with 2 showers where baths are infrequent.

Some are, some have an integral unvented cylinder inside the box too.

The only one I've seen is the Keston Duet, but there isn't an overall box.
You can see the separate cylinder, boiler and framework. Are there any other
makes? I would have thought that an integrated heat bank would generally
make more sense for a unit designed down to a small size in a common casing,
especially when they'd rather they could be installed by a CORGI without
further qualifications.

Christian.