What is the difference between 夜(yè) and 晚 (wǎn)?
Originally,  晚 could be written as 莫 (in ancient form): 艹（草, grass）+ 日 (sun), referring to when the sun is below the grass -- sunset. 

In modern Chinese, we can understand or memorize it in this way: 日 (sun) + 免 (cancel), without the sun, sunset.  

Then its meaning extends to night and evening. So 晚 does mean night and evening, and they are its original meanings!

Originally, 夜 could be written as 亱 (in ancient form): house (dot + horizontal) people (人, Throw away + vertical) + day (旦), referring to (people, sun) stop and rest. It means the time period from dusk till dawn. 

Just as 晚，its meaning extends to night and evening.

晚 is more focused on "being late" (at night or in the evening), which is later used as "late".
夜 is more focused on "dark and dusk" (at night or in the evening). 

Therefore, “夜晚” can be understood in 2 ways:

(1) in Modern Chinese, night or evening, together as a noun; 

(2) as noun+adj: the night/evening is late → the time at night is late. 



晚 means:


Noun. 

(1) (形声。从日,免声。本义:傍晚;黄昏)

(2) 同本义 [evening]

晚,莫也。——《说文》

晚,暮也。——《广韵》

四时失序,则辰星作异。…政急则出蚤,政缓则出晚。——《汉书·李寻传》

一屠晚归。——《聊斋志异·狼三则》

(3) 又如:晚曦(晚霞);晚夕(傍晚,晚上);晚半天儿(晚夕,晚晌,晚间,晚上);晚钟(傍晚的钟声);晚寒(傍晚的寒气);晚晴;晚饷(晚餐);晚阴(傍晚时的阴霾);晚来(傍晚) [evening]

(4) 夜晚 [night] 

晚星没。——庾信《对烛赋》

(5) 又如:晚吹(夜晚的风);晚头(晚上);晚月(夜月);晚炬(夜间的火炬);晚漏(晚更);晚魄(月亮);晚逻(夜间巡逻) [night] 

(6) 晚年 [old age;one’s later years]

晚出榆关逐北征,惊沙飞迸冲貂袍。—— 温庭筠《塞寒行》

(7) 又如:晚运(晚年。运指时期);晚涂(晚年);晚境(晚年的境遇;晚年);晚悟(晚年觉悟) [old age;one’s later years]

(8) 秋季 [antumn]。如:晚菘(秋末冬初的大白菜);晚造(秋季作物);晚果(秋天成熟的果实);晚热(秋天的炎热)

(9) 旧时官场后辈对前辈、下级对上级称晚生,简言曰晚。多用于书信 [pupil (often self-reference in writing or speaking to teacher)]

恕治晚不能躬送了。——《儒林外史》

(10) 时间靠后。属于或关于时间上或发展上的后期阶段的 [late;far on in time]

兴尽晚归舟。——宋· 李清照《如梦令》

事之晚矣。——《资治通鉴·汉纪》

土气有早晚。——宋· 沈括《梦溪笔谈》

(11) 又如:晚唐;晚父;晚母(后母;继母);晚爷(后父);晚妻(后续之妻);晚嫁(再嫁);晚伯母(伯父后来续娶的妻子);晚进(后进;后辈);晚婆(晚娘,继母) [late;far on in time]
Adj.

(1) 迟,在规定的、通常的或恰当的时间以后来的或做的 [late]

大器晚成。——《老子》四十一章  Chapter 41.

(2) 又如:晚达(显达较迟);晚日(近日;最近几天);晚歇(〈方〉∶过一会儿);晚转身(〈方〉∶第二次嫁人);晚客;晚茶(迟采摘的茶叶);晚麦(迟熟的麦);晚代(近世);晚禾(晚稻);晚甲(迟发的芽)

(3) 衰;老 [old]。如:晚叶(晚年;老叶);晚谬(年老昏愦);晚暮(年老)




夜 means:


Noun. 

(1) (形声。金文字形。从月,亦声。本义:从天黑到天亮的时间) [Origin: The time interval from dusk till dawn]  

(2) 同本义 [night]

夜,舍也。天下休舍也。——《说文》

夜,暮也。——《广雅》

昨夜见军帖。——《乐府诗集·木兰诗》

三日三夜。——《世说新语·自新》

(3) 又如:夜游子(爱在晚上游荡的人);夜里个(昨天);夜合钱(妓女接客所收的报酬);夜行人(夜间秘密行事的人,如盗贼、侠客之类);夜不收(夜间侦探;亦指夜晚淫乐者);夜叉婆(凶暴貌丑的女人);夜消(夜宵);夜里(昨天晚上);夜台(长夜台。墓穴);夜夫(更夫);夜漫漫(黑夜漫长。喻指苦难的岁月);。又如:夜艾(夜深深);夜永(夜深);夜定(指夜深人静之时) [night]

(4) 黄昏,天黑 [dusk]

岂不夙夜?谓行多露。——《诗·召南·行露》

行者怏怏自退,看看日色早已夜了。便道此时将暗,也寻不见师父,不如把几面镜子细看一回。——《西游补》

(5) 凌晨,天快要亮的时候 [in the small hours;before dawn]

郑玄注:“夜,夜漏未尽鸡鸣时也。”
Adj. 

(1) 晦暝,幽暗 [dim;dusky]

是故索物于夜室者,莫良于火;索道于当世者,莫良于典。——《潜夫论》

(2) 又如:夜室(黑暗的房间;墓穴);夜台(夜庭。坟墓。亦借指阴间);夜府(犹夜台,墓穴)