The blue dye that comes from indigo and woad plants is surprisingly the same. what makes woad dye blue is called “indigotin”. Woad contains this. Indigo contains this. And almost 300 other plants also contain enough indigotin to be usable to dye blue. Sometimes “Indigo” refers to types of Indigofera, and sometimes it refers to a variety of other plants from China, Nigeria or Japan. All dye the colour named ‘Indigo blue’ through the indigotin they contain. And it seems woad does the same. The major difference appears to be the concentration of indigotin in the plant material. Woad is less concentrated in indigotin than Indigo itself is, meaning more has to be used, which is presumably why Indigo started to become more popular than woad in Europe in the 16th century, after it was introduced from Asia.

Source: A Viking's Life For Me Indigo vs. Woad: What’s the Difference?