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You can use Shortest if the sub-strings of the form <td, class=test, >...</td> don't contain nested sub-strings of the form <td, class=test, > or </td>. If they do, follow this link.

v = "...<td, class=test, >strings1</td>...<td, class=test, >strings2</td>..";
StringCases[v, Shortest["<td, class=test, >" ~~ x__ ~~ "</td>"] -> x]

{"strings1", "strings2"}

You can use Shortest if the sub-strings of the form <td, class=test, >...</td> don't contain nested sub-strings of the form <td, class=test, > or </td>. If they do, follow this link.

v = "...<td, class=test, >strings1</td>...<td, class=test, >strings2</td>..";
StringCases[v, Shortest["<td, class=test, >" ~~ x__ ~~ "</td>"] -> x]

{"strings1", "strings2"}

You can use Shortest if the substrings of the form <td, class=test, >...</td> don't contain nested sub-strings of the form <td, class=test, > or </td>. If they do, follow this link.

v = "...<td, class=test, >strings1</td>...<td, class=test, >strings2</td>..";
StringCases[v, Shortest["<td, class=test, >" ~~ x__ ~~ "</td>"] -> x]

{"strings1", "strings2"}

You can use Shortest if the sub-strings of the form <td, class=test, >...</td> don't contain nested sub-strings of the form <td, class=test, > or </td>. If they do, follow this link.

v = "...<td, class=test, >strings1</td>...<td, class=test, >strings2</td>..";
StringCases[v, Shortest["<td, class=test, >" ~~ x__ ~~ "</td>"] -> x]

{"strings1", "strings2"}

You want to use Shortest.

v = "...<td, class=test, >strings1</td>...<td, class=test, >strings2</td>..";
StringCases[v, Shortest["class=test, >" ~~ x__ ~~ "</td>"] -> x]

{"strings1", "strings2"}

You can use Shortest if the substrings of the form <td, class=test, >...</td> don't contain nested sub-strings of the form <td, class=test, > or </td>. If they do, follow this link.

v = "...<td, class=test, >strings1</td>...<td, class=test, >strings2</td>..";
StringCases[v, Shortest["<td, class=test, >" ~~ x__ ~~ "</td>"] -> x]

{"strings1", "strings2"}