The two are separate in the sense that you pay Pay As You Earn (PAYE) and National Insurance Contributions (NIC) on your employment which is deducted from your pay but the Income Tax on the profits from your web design business is payable in two instalments on 31 January and 31 July together with an adjustment of any balance owing the following 31 January.
You have three months from the date of commencement to notify your Tax District that you have started a business. You can find all the details and do the registration process from the .gov.uk website here.
At the end of the tax year in which you commenced trading in your own business you must complete a Tax Return including a Self Employment section for the web design business. Basically if your turnover (or sales) is under £15,000 you only need to fill in figures for turnover, expenses and profits. If the turnover is greater than £15,000 detailed profit and loss and balance sheet figures are required. Profits for the period up to 5 April after you started (and subsequent annual accounting periods) will be subject to Income Tax and National Insurance Contributions. Self employed payments of Tax and National Insurance Contributions are required twice yearly – by 31 January and 31 July.
The Basic NIC is called Class 2 and it is usually paid by direct debit in four or five weekly instalments. But if your self-employed earnings are less than the threhshold no Class 2 is payable. The additional NIC is called Class 4. For 2018/19 tax year the thresholds are 9% on profits between £8,424 and £46,350 and 2% on profits over £46,350
It might be simpler to apply to HM Revenue and Customs (HMRC) for a deferment using form CA72A in HMRC leaflet CA72. This has the effect of deferring payment to after the tax year when the total NIC liability can be accurately determined.
Once the Income Tax and NIC liability is determined it is usual to pay in the two instalments mentioned above. In your situation where your web design business is not generating a regular income it would be inadvisable to pay through the tax code number and have the self-employed liability deducted from your full time earnings. However, you should remember to set aside a percentage of your web design business sales to pay for the tax and NIC liability. This is best done by transferring, say 20 to 25 per cent to a separate bank account.