Not sure where U see the word "距", but it does not mean "He/She" (佢). 距 usually means distance (距離). However, the pronunciation of "He/She 佢“ is same to "距”. As the others said, maybe someone would use 距 instead of 佢 on internet chatting / sms etc becos of easily typing or other reasons. 佢嘅 ＝ HIS/HER We use it as spoken language. 他(她)的 = HIS/HER we use it literary or as written language. for example, "His cup" In Cantonese, ppl say "佢嘅杯“ but if ppl have to write this down in a proper way (i don mean for internet chatting or sms) then ppl write "他的杯子” in Mandarin, ppl say and write also "他的..."

That is the problem of the difference between writing practice in Canton prefecture or in Hong Kong. The writing of modern Cantonese is not very standardized due to different source of ancient books or records. For the ease of pronunciation and reading, many of the characters are changed from its original form to the one you are reading nowadays. The pronunciation is the only matters, even you write "渠既" will also be "ok" though that might be a bit odd. It doesn't matter because most of the formal articles are in Chinese (pekingese) in stead of Cantonese. Written Cantonese is main for casual purposes like chatting or easy local publications.

The word (佢嘅) is mostly used in casual forum and internet chatting because most Cantonese user tend to speak informally. (他的) is a word only be used in official paper or literature, like(她的/它的/牠的), People never use it in live talking. In addition, most people on the internet rather use(佢既) than (佢嘅) because former one is easier to type and it applies to many other situation. Typing (距) is fine to use on internet, every Cantonese speaker would understand it but just a little bit less common than (佢). Although (渠) should be this correct form of (佢), noone use it or even know it nowadays.

佢=距=he/she (Cantonese) 他/她=he/she(Mandarin, and formal writing in cantonese )