What's the initial and regular duration for the plan? If it's by calendar year what's the start month and day? Does the dates for the subscription within CBSubs > Subscriptions look correct?

Do you have an initial price/duration that's different from the regular price/duration? The "then" is supposed to indicate that. Can also happen if using "Bonus time before first period start (for calendar-based durations)" on by calendar durations.

I have just noticed another interesting one:
11/09/17 - 11/09/18, then 11/09/18 - 11/09/19

That one looks ok.

with the first one, they were lapsed for a long while and had a discount in their first year.

Ah, that could be it. Is the plan set to renew from expiration date or when paid? Specifically what is "Manual renewal extends expiration date as follows" set to?

In the second one, why do we reference next year? It initially gives the impression that they are a member for 2 years. We really only want to mention their start/stop date.

If it's a recurring subscription and not a single payment and you've an initial price/duration then it shows both periods. Single payments may also show both, but I don't really see a reason to unless it's by calendar and bonus time is configured.