You can use dot-broadcasting to evaluate distances, and either a table library or DataFrames for tabulated printing:
julia> using StringDistances, DataFrames
julia> x = ["ap p le", "or an ge", "ap pl e", "ap pl e", "or an ge", "ho ne yc ri sp ap pl e"];
julia> y = ["ho ne yc ri sp ap pl e", "ho ne yc ri sp ap pl e", "or an ge", "ap pl e", "or an ge", "ho ne yc ri sp ap pl e"];
julia> dist = evaluate.((Jaccard(2),), x, y);
julia> DataFrame(x = x, y = y, JaccardDistances = dist)
6×3 DataFrame
│ Row │ x │ y │ JaccardDistances │
│ │ String │ String │ Float64 │
├─────┼────────────────────────┼────────────────────────┼──────────────────┤
│ 1 │ ap p le │ ho ne yc ri sp ap pl e │ 0.863636 │
│ 2 │ or an ge │ ho ne yc ri sp ap pl e │ 0.961538 │
│ 3 │ ap pl e │ or an ge │ 1.0 │
│ 4 │ ap pl e │ ap pl e │ 0.0 │
│ 5 │ or an ge │ or an ge │ 0.0 │
│ 6 │ ho ne yc ri sp ap pl e │ ho ne yc ri sp ap pl e │ 0.0 │