The Islamic veil symbolizes the spiritual protection of the Muslims. As the women represent the spiritual body of the Islamic society, this veil takes a palpable form in the case of women while it remains intangible in the case of men. Women need protection from external dangers and this is why their veil is manifest because it represents their external protection while for men the veil is concealed because it represents their internal protection. But it must always be remembered that observing the veil is an obligation for both men and women alike, even if it assumes different forms.
We notice that in the above quoted verses, after the mention of the commandments to men and women separately, the Quran ends this by saying:
And turn ye to Allah all together, O believers that you may prosper.
This emphasizes the fact that for the achievement of the sought results, both men and women need to carry out their share of responsibilities in connection with these injunctions. Or, in other words, like the soul and body, men and women complement one another and they will have to work together to act upon these commandments for the sake of the prosperity of their society as one unit. It is a sort of a blessing which can only be acquired by the joint efforts of men and women.
Yet comparing the two verses reveals another point of interest. The directions concerning the believing men ends with the words: that is purer for them. Surely, Allah is well-aware of what they do which means that if the believing men obey this command, they will be able to purify their souls. God knows well their intentions and the results of their actions, so they should do their best to observe this command and if they are sincere in their efforts, God will bless these efforts and will grant them success. But the order concerning the believing women does not end with a similar statement.
This is to hint to the believing women that there are still some more requirements that they will need to fulfil before they can achieve fruitful results. These requirements are mentioned separately in the verses that directly follow the above verses because they can only be complied with by the combined action of the men and women together. Those verses instruct the believers to arrange marriages for the women having no husbands. This emphasizes the fact that the real duty of the woman in the society can only be carried out fully after she becomes a housewife. This point will be further clarified when one understands the true role of the woman in society.