A tank top I always assume to be like a vest or undershirt, anything that goes over a regular shirt is a cardigan or gilet, of which I have a couple, one a reversible hi-viz with a plain fleece on the other side, the other a Fox Racing fleece I bought in Chamonix back in the 90’s, and still wear it a lot, ideal for this time of year. It didn’t have hand warmer pockets, so a friend of mine added two zipped front pockets, which makes it even mor useful now.
Oh, and I have a couple of down ‘vests’, as Americans call them, or gilets, as everyone else does.
Again ideal for this time of year.