There is only one spelling for panic; the verb is inflected 'panic, panics, panicked, and panicking’. The form panick is used for progressive tense, past tense and past participle. We don't write panick today, though English speakers from a few hundred years ago might have (in the same way they might have written musick).
When the alternate spelling “panick” is used for the past participle: "I panicked last night at the disco." When it’s use for progressive tense: “Invariably, when markets are panicking, they sell the stocks quickly.”
It's the rule for root words ending in "c" is that you have to add “k”, so the spelling is related with the pronunciation. If we don't add the <k>, it looks as if the <c> has to be pronounced /s/. If the "k" was not there, “panicing” would look like the word which is supposed to be pronounced as if it is ended in "sing," while “paniced” would be pronounced like “panised”.
At the request of several families he and Mrs Legge gave a home for some months to a young Dutch girl, a granddaughter of the first Dutch governor of the Straits Settlements. She had several pearls of which the Dutch residents were great collectors, got from oysters found in a river of the Malay Peninsula, when she left them she gave Mrs Legge a small box containing a large pearl the size of a pea, with a blue spot on it, and two others not so large. This box was then put away and locked up. Several weeks later he took it out and on opening it discovered more than a dozen pearls, most of them very small. Astonished at the phenomenon he called his chief servant, a Portuguese, who happened to enter the room and who expressed no surprise but declared it to be a common occurrence. On enquiry he found that many of the Dutch people had jars of pearls, large and small, which had accumulated in this way. Some years later he related the incident at dinner on board ship. The captain was a cauti…