The Wash Act was passed by Parliament in 1784. The 1823 act is more correctly referred to as an Excise Act (although since the 1784 act was an excise act as well, I can understand the confusion). The later act was based on the findings of the 'Commission of Inquiry into the Revenue' chaired by Lord Wallace. It made many very significant changes in the way the industry was taxed and regulated (including reducing the duty on spirits to two shillings and five pence per gallon - that's about 12p in today's money). Basically, it laid the foundations for the whole of the modern whisky industry, resulting in the rapid demise of illicit distilling and an equally rapid growth in the number of legal distilleries in the following years. [ib 75/q3.98]
To my knowledge, there was no Wash Act in 1823. The Wash Act of 1784 drew the line between the Lowlands and Highlands. In the Highlands, duty was charged on the capacity of the still; in the Lowlands, there was tax per gallon on the wash. The Excise Act of 1823 permitted whisky distilling upon paying a fixed licence fee of £10 plus payment per gallon distilled. [ak 75/q3.98]