Raceme:   An unbranched, elongated arrangement of flowers borne on pedicels (or capitula borne on peduncles), in which the flowers/capitula mature from the proximal end to the distal end.   In the image below of Symphyotrichum racemosum, each branch is considered an "inflorescence".

Racemiform:  Having the appearance, but not necessarily meeting the strict definition of a raceme.  In the example shown, the inflorescence branches are "racemiform", though not strictly "racemes", for the capitula mature from distal end to proximal end.