The A308(M) is a short spur from the M4 near Maidenhead, and is the second spur to begin at the confusingly-numbered junction 8/9.
Initially the M4 had a junction, number 8, with the A308 south of Maidenhead. When it was extended west towards Reading, a new interchange was required to connect to the original line of the motorway, what is now the A404(M). That new junction was too close to junction 8 so junction 8 was closed, being replaced by a short spur road from the new junction back to the A308. That short spur is the A308(M), and it is the reason the new junction is number 8 as well as number 9.
For a long time, this little spur was probably the UK's shortest motorway. It's about half a mile long, and it has one straight section and one curve, which means that the eastbound carriageway, running around the outside of the corner, is marginally longer than the westbound. But the argument over the UK's shortest motorway rested on a knife edge and depended very much on how to measure the length of a route, because the other candidate - the A64(M), an urban motorway in Leeds - has one carriageway significantly longer than the other and some uncertainty over where exactly it starts. Luckily that argument is now settled thanks to the much newer A8(M) near Glasgow, which is far shorter than either of them and leaves the A308(M) fighting for second place.
The whole situation is fraught with uncertainty, and the only thing you can be sure of is that you won't have time to figure it out on your short trip along the A308(M).