Mecha-Arm (メカアーム) is, as its name implies, a mechanical arm that is found in Mega Man X2. It first appears in the opening stage and again in Violen's X-Hunter stage. They tend to grab X, and either drop him back a bit or into a damaging areas. So, X needs to keep moving to avoid getting grabbed.
Arm (アーム) is a variety of the Mecha-Arm that appears in the opening stage of Mega Man Xtreme 2. Unlike the Mecha-Arm, it attacks by shooting at the player and can be destroyed.