Are reactivity series the same as metal activity series?
They are the same - but be careful not to confuse reactivity series with the term reactivity!!!
The activity series tells us how likely a metal atom is to participate in a single replacement reaction. The activity series may also be referred to as the reactivity series. Most textbooks in the US that I've used in my teaching use the term activity series of metals.
Here is a video which provides examples of how the activity series can be determined experimentally.
Be careful not to confuse this with the term reactivity which is much more general and refers to how likely atoms of an element are to participate in any type of chemical reaction.
Hope this helps!