I've only traveled by ferry, because I found the Eurotunnel too expensive just for 15 minutes less of a trip.and I prefer floating boats over under-the-sea small train tunnels.

I'll quote the Dover to Calais ferries website:

If I miss my sailing, can I get on another ferry? Yes you can, if we’ve got room and your ticket type is flexible. Check out the terms and conditions, paragraph 4iii) and our Which Ticket? Page for the details.

that paragraph:

What will I be charged at port for not travelling as booked?

£20 amendment fee + re-price

and about the arriving 2 hours ealier thing:

i. We can only guarantee availability including that of passengers, vehicle and extras, on your booked departure dates and times. Additional surcharges may apply for travel at other times. Refunds will be subject to ticket type.

My brother used the tunnel recently, managed to check in a few minutes late for the one direction and with a few minutes spare in the other direction.

When late he was told he could no longer use the train he had booked, the next was completely booked but he was put on the next, so one hour after the one he had booked for.
If it had been very busy all day, he would still have been put on the first available train, which might have been one late in the evening instead of his missed morning one.
He was also told that the price you paid for the ticket booked is the price you get to cross, even if you go from a lower to a higher price time.

Most ferries have a like policy, but not all. I am not familiar enough with the different ferries to be sure where you can 'miss' your slot and be put on the next available and where a missed slot will make you pay again.

When you check prices, do check all, as often the prices depend on how many others have booked for that same crossing/time, more than on the average price for that crossing.