Answer:
They all have to do with counting.
月 GETSU, GATSU, tsuki - moon, month - counter for months
員 IN - member - counter for members of a group
歩 HO, BU, aru(ku), ayu(mu) - walk - counter for steps
銭 SEN, zeni - money, loose change, 1/100yen - counter for money
層 SOU - layer - counter for layers