Glyph origin of 「凉」 and its relation with 「涼」
李学勤《字源》 says:

谷衍奎《汉字源流字典》 says:

According to them, 涼 was the standard form and 凉 was the vernacular form with the same meanings. The People's Republic of China prescribed that 凉 should be the standard form and 涼 should be the obsolete variation form (异体字).
In Taiwan, 涼 is still the standard form and 凉 is 异体字. See 重編國語辭典修訂本: 凉 涼
According to the same sources, 凄 has a similar story but is a little more complicated, because PRC prescribed that 凄 should be the standard form for both 淒 and 悽. This also did not happen in Taiwan (you can't even find 凄 in 重編國語辭典修訂本).