The Blessing Cross is a Hand-held Cross and tends to be used more by Orthodox, Anglican and Catholic priests than Protestant clergy. Therefore whilst any type of cross could be used, the most common is a crucifix, a Budded Cross or an Eastern Cross. The lower bud of the Budded Cross, or foot-support (see suppedaneum) of the Eastern Cross, gives a convenient separator between the cross part and the handle part.
The Blessing Cross is considerably smaller than another portable cross - the Processional Cross. The Blessing Cross may be used like a conductor's baton to make a Sign of the Cross over a supplicant, congregation, or some object being blessed. The cross may be kissed by the faithful, or the priest may just tap them on the head (lightly!) with it. (See also 'Priest Stick' in Buddhist fish symbol).
Christians often carry their own Hand-held Cross and kiss it at the start and end of prayer. This is sometimes referred to as a Palm Cross, since it fits in the palm of the hand. On this website, we describe the Palm Cross made from green palm leaves for Palm Sunday celebrations. (The dual use of the word 'palm' stems from the shape of the palm's leaves, growing like the fingers of an open hand.)
Alex Roman tells us of olive wood palm crosses made by Christians in Palestine for vistors to take back as souvenirs. (See also the Compostelan Cross.) Medieval pilgrims to the Holy Land wore small palm Crosses on their clothing as they returned home.
From this tradition came an alternative English name for a pilgrim: 'Palmer'. This later became used as a surname.