Exactly as the OP suspects ..
Typically on a foreign exchange -related trading site, or something like ofx.com, it's totally normal that - as you guess - the price might be a little different from when you literally click the button.
Note that interestingly this can even happen on Expedia (!) when you buy an air ticket.
Typically the flow goes like this:
It will state "blah $123" and there will be a warning on the screen, "this may change slightly"
You click "Execute" and
There now appears on the screen: "Exact amount will be $122.98, you have (countdown) 7 seconds to agree"
Of course, the exact web interface can vary. I've seen some that use the approach "Your exact price was -blah-, you have N seconds to cancel that if you're unhappy."
Other dealers will just outright state "the price may change slightly if you're slow and it's tough luck, take it or leave it."
There is simply no "standard answer" but yes, as the OP suspects the situation is dynamic.
On Coinbase as in your example ...
In fact as it happens on that site they do in fact promise you the exact price shown, for some limit of seconds. (They take the small risk on small price changes.)
FYI regarding "trading options"
A related issue. There are 1000 questions on this site relating to the confusion of the "price" of stocks and derivatives. If you're looking at the " ' price ' " of some thinly traded stock instrument, the " ' price ' " shown is nothing more than whatever happened to be the most recent price of an actual trade. This has absolutely no relationship to what you may or may not be able to sell or buy for, "now".
Note that in your example, you are literally selling/buying from Coinbase. It is quite simply "a dealer". It's not a brokerage/market type situation where you are selling/buying from a pool of other users.
And, as it happens, they do guarantee the "on-screen" price. Unlike, say, Expedia where you can get a "the price is now ..." message.