Different Plot Legend Style in the Plot with same code and How to make it good-looking inside the figure

Question

I use Plot to draw two figures and combine them in one figure with the following code.

C1 = Plot[{((3 t + 1/2)^2 (1 - 2 t 1/4))/(18 t) + 2 t^3 (1)^2 (1/4)^3}, {t, 1/6 (3 - Sqrt[3]), 2}, 
    PlotTheme -> "Scientific", PlotRange -> Automatic, FrameLabel -> {{HoldForm[SubsuperscriptBox["\[Pi]", "i", "*"] // DisplayForm], None}, {HoldForm[t], None}}, 
    LabelStyle -> {GrayLevel[0]}, PlotStyle -> {Red}, 
    PlotLegends -> {"\!\(\*SubsuperscriptBox[\(\[Pi]\), \(A\), \(*\)]\) \under \!\(\*SubscriptBox[\(\[Alpha]\), \(A\)]\)=1"}]

D1 = Plot[{((3 t - 1/2)^2 (1 - 2 t (1/4)))/(18 t) + 2 t^3 (1)^2 (1/4)^3}, {t, (1/6) (3 - \[Sqrt]3), 2}, 
    PlotTheme -> "Scientific", PlotRange -> Automatic, FrameLabel -> {{HoldForm[SubsuperscriptBox["\[Pi]", "i", "*"] // DisplayForm], None}, {HoldForm[t], None}}, PlotStyle -> {Dashed, Red}, 
    PlotLegends -> {"\!\(\*SubsuperscriptBox[\(\[Pi]\), \(B\), \(*\)]\) \under \!\(\*SubscriptBox[\(\[Alpha]\), \(B\)]\)=1"}]

Show[C1, D1, PlotRange -> All]

However, the font styles of the plot legend are different as shown in the picture even if I used the same PlotLegends in the code and I have tried LegendMaker and autoLegendto make the legend look nice but failed. How can I adjust or rewrite the code to make the plot legends look the same or achieve the effect of autoplot putting the legends on the right-bottom side of the figure? Thanks in advance.

In addition, how can I put the plot legend in the rounded rectangle with a grey background-color as shown in the example picture below?

Answer 1

An alternative that allows to put the legend in the lower right corner (or everywhere for that matter):

Plot[{((3 t + 1/2)^2 (1 - 2 t 1/4))/(18 t) + 
   2 t^3 (1)^2 (1/4)^3, ((3 t - 1/2)^2 (1 - 2 t (1/4)))/(18 t) + 
   2 t^3 (1)^2 (1/4)^3}, {t, 1/6 (3 - Sqrt[3]), 2}, 
 PlotTheme -> "Scientific", PlotRange -> All, 
 FrameLabel -> {HoldForm[t], 
   HoldForm[SubsuperscriptBox["\[Pi]", "i", "*"] // DisplayForm]}, 
 PlotStyle -> {Red, {Dashed, Red}},
 PlotLegends -> 
  Placed[LineLegend[{"\!\(\*SubsuperscriptBox[\(\[Pi]\), \(A\), \
\(*\)]\) under \!\(\*SubscriptBox[\(\[Alpha]\), \(A\)]\)=1", 
     "\!\(\*SubsuperscriptBox[\(\[Pi]\), \(B\), \(*\)]\) under \
\!\(\*SubscriptBox[\(\[Alpha]\), \(B\)]\)=1"}, 
    LegendLayout -> 
     Function[{x}, Grid[x, Spacings -> {0.6, 0}, Alignment -> Left]], 
    LegendMarkerSize -> {22, 12}], {0.8, 0.2}]]

The last parenthesis in the Placed command controls where you want the legend to appear.

To add a box around the legend, as requested in the comments, use:

Plot[{((3 t + 1/2)^2 (1 - 2 t 1/4))/(18 t) + 
   2 t^3 (1)^2 (1/4)^3, ((3 t - 1/2)^2 (1 - 2 t (1/4)))/(18 t) + 
   2 t^3 (1)^2 (1/4)^3}, {t, 1/6 (3 - Sqrt[3]), 2}, 
 PlotTheme -> "Scientific", PlotRange -> All, 
 FrameLabel -> {HoldForm[t], 
   HoldForm[SubsuperscriptBox["\[Pi]", "i", "*"] // DisplayForm]}, 
 PlotStyle -> {Red, {Dashed, Red}}, 
 PlotLegends -> 
  Placed[LineLegend[{"\!\(\*SubsuperscriptBox[\(\[Pi]\), \(A\), \
\(*\)]\) under \!\(\*SubscriptBox[\(\[Alpha]\), \(A\)]\)=1", 
     "\!\(\*SubsuperscriptBox[\(\[Pi]\), \(B\), \(*\)]\) under \
\!\(\*SubscriptBox[\(\[Alpha]\), \(B\)]\)=1"}, 
    LegendLayout -> 
     Function[{x}, Grid[x, Spacings -> {0.6, 0}, Alignment -> Left]], 
    LegendMarkerSize -> {22, 12}, 
    LegendFunction -> (Framed[#, 
        FrameStyle -> Directive[Thickness[.05]], RoundingRadius -> 4, 
        Background -> RGBColor[.95, .95, .95, 1]] &)], {0.75, 0.2}]]

Answer 2

Use a single Plot

Clear["Global`*"]

Plot[{
  ((3 t + 1/2)^2 (1 - 2 t 1/4))/(18 t) + 2 t^3 (1)^2 (1/4)^3,
  ((3 t - 1/2)^2 (1 - 2 t (1/4)))/(18 t) + 2 t^3 (1)^2 (1/4)^3}, {t, 
  1/6 (3 - Sqrt[3]), 2},
 PlotTheme -> "Scientific",
 PlotRange -> All,
 FrameLabel -> {HoldForm[t],
   HoldForm[SubsuperscriptBox["π", "i", "*"] // DisplayForm]},
 PlotStyle -> {Red, {Dashed, Red}},
 PlotLegends -> {
   "\!\(\*SubsuperscriptBox[\(π\), \(A\), \(*\)]\) under \
\!\(\*SubscriptBox[\(α\), \(A\)]\)=1",
   "\!\(\*SubsuperscriptBox[\(π\), \(B\), \(*\)]\) under \
\!\(\*SubscriptBox[\(α\), \(B\)]\)=1"}]