If transferring from one wallet to another, will that be categorized as the purchase of crypto?

It is dependent on the wallet from which you are sending money.

If you are moving funds from one offline wallet to another offline wallet that is owned by the same person, there is no tax. Whereas if you are moving funds from your offline wallet to some other person's wallet then tax and TDS both are applicable. And, in the case of an online wallet, every transfer is taxable, regardless of whether money is sent to yourself or to someone else.