Salaah time expiring while one is performing Salaah

If salah was delayed nearing to the end of its time and the takbeer for commencing the salah was made within the time, for example within dhuhr time, however, the salah was completed when asr time set in then will the salah be counted as a qadha salah or will it officially count and also will this count as missing salah within its time thus meaning one is sinful or will it be sinful for other reasons such as the sin for delaying and is there a difference in severity between these two sins?