Cell cycle arrest and apoptosis are both likely responses to certain events, such as radiation, and the pathways involved do overlap somehow. But there is little agreement over sequential links from cycle arrest to cell death. It is still an open subject, see for example: Aubrey BJ, Kelly GL, Janic A, Herold MJ, Strasser A. How does p53 induce apoptosis and how does this relate to p53-mediated tumour suppression? Cell Death Differ. 2018 Jan;25(1):104-113.
Cell cycle arrest in response to DNA damage-->p53-->cell cycle inhibitor expression (p21) are ways to safe gaurd cells from DNA damage by DNA repair (this is when the cells undergo arrest), but when the damage is severe, mitochondrial mechanisms kicks-in to convert the cell cycle arrest signal into apoptosis signal, where p53 directly and indirectly through Bax target mitochondrial membrane potential. So the threshold of DNA damage and length of DNA repair time determines the cell cycle arrest OR cell cycle arrest+apoptosis routes. Alternatively cells escape from apoptosis by undergoing cell cycle arrest, especially at G1-S phase. This usually happens in therapeutic settings, where mTOR inhibition plays a role. Example rapamycin..
Cell cell cycle arrest occurs when cell is in stress or have a danaged DNA, this arrest happenes so that DNA repair machinery can have time to repair danaged DNA to avoid apoptosis. However, if the damage is so intense than cell is switched to Apoptosis. P53 is a major switch in this regard.
Cell cycle arrest is the first response to DNA damage or some stress conditions. DNA damage => ATM/ATR => p53. p53 is the decisive protein, this is why it called "guardian of the genome". Low level of p53 is the transcription factor for p21 which is known as a CDK inhibitor. This process makes time for DNA repair proteins. If the damage is excessive p53 concentration increase and transcribes apoptotic proteins (bax, puma etc.). There is two scenario in your question. First, cell cycle arrest may not induce apoptosis, it is one of the steps in apoptotic process. In second senario which is about cell cycle arrest pathway. If you tell how cell cycle arrest occured, then we can talk about the pathway.
Similar stimuli can induce both cell cycle arrest or apoptosis. These stimuli induce cellular stress (very often genes like p53 are induced). In many cases cell cycle arrest gives time to repair stress induced cell damage (e.g. DNA damage, oxidative damage). If this is not possible cells undergo apoptosis. Thus, cellular stress can induce cell cycle arrest and can end up in apoptosis but is has not induce cell death.
Cell cicle arrest as a consequence of stress whether chemical, or physical determines intracellular acidification. This is the main reason of cell death.