I think from your description there is a compression joint between the metal piping of the old shower and the existing pipework.
I think you look through the link gave you it covers all the eventualities - what I generally do is buy a range of compression joint options and see which one is best for the task as I find it hard to remember the details. hen I take back the ones I haven't used for a refund. Works with B&Q, anyway.
Seriously, you're going to have to read thriugh the guides and work out what you need as it's practically impossible this way. But I think it's the case that 'compression unit' means 'compression joint'.