RegionMember work for Interval.

f = Piecewise[{{1, RegionMember[Interval[{0, 1}]]@{x}}}, 0];
g = Piecewise[{{1, 0 < x < 1}}, 0];
 
Plot[{f, g}, {x, 0, 2}, 
 PlotStyle -> {Directive[Red, Opacity[.2], AbsoluteThickness[10]], 
   Blue}]

When we want to use Element, we need to write such as Element[{1/2}, Interval[{0, 1}]] (*True *).

h = Piecewise[{{1, Element[{x}, Interval[{0, 1}]]}}, 0];
Plot[h, {x, 0, 2}]

• RegionMember work for Interval.

f = Piecewise[{{1, RegionMember[Interval[{0, 1}]]@{x}}}, 0];
g = Piecewise[{{1, 0 < x < 1}}, 0];
Plot[{f, g}, {x, 0, 2}, 
 PlotStyle -> {Directive[Red, Opacity[.2], AbsoluteThickness[10]], 
   Blue}]

• When we want to use Element, we need to write such as Element[{1/2}, Interval[{0, 1}]] (*True *).

h = Piecewise[{{1, Element[{x}, Interval[{0, 1}]]}}, 0];
Plot[h, {x, 0, 2}]

RegionMember work for Interval.

f = Piecewise[{{1, RegionMember[Interval[{0, 1}]]@{x}}}, 0];
g = Piecewise[{{1, 0 < x < 1}}, 0];
Plot[{f, g}, {x, 0, 2}, 
 PlotStyle -> {Directive[Red, Opacity[.2], AbsoluteThickness[10]], 
   Blue}]

RegionMember work for Interval.

f = Piecewise[{{1, RegionMember[Interval[{0, 1}]]@{x}}}, 0];
g = Piecewise[{{1, 0 < x < 1}}, 0]; 

Plot[{f, g}, {x, 0, 2}, 
 PlotStyle -> {Directive[Red, Opacity[.2], AbsoluteThickness[10]], 
   Blue}]

When we want to use Element, we need to write such as Element[{1/2}, Interval[{0, 1}]] (*True *).

h = Piecewise[{{1, Element[{x}, Interval[{0, 1}]]}}, 0];
Plot[h, {x, 0, 2}]