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The e-visa does not allow extensions, vs. the normal visit visa. They are both valid for 3 months (initial stay).
There is an additional fee for the e-visa (it may not apply to everyone). The fee is 3 Kuwaiti Dinars (around 10 USD).
There is a practical difference when you land. To get a visa on arrival, you have to go to the visa issuance desk - get your visa, and then go through the immigration queue.
If you have the visa confirmation on hand (online e-visa), you can just go directly through immigration.
E-visas are still relatively new for Kuwait; thus the mismatch in Timatic. They are available even for UK passport holders; the list of eligible passport holders is mentioned at the e-visa main page:
ANDORRA AUSTRALIA AUSTRIA BELGIUM
BHUTAN BRUNEI BULGARIA CAMBODIA
CANADA CROATIA CYPRUS CZECH
DENMARK ESTONIA FINLAND FRANCE
GEORGIA GERMANY GREECE HUNGARY
ICELAND IRELAND ITALY JAPAN
LAOS LATVIA LIECHTENSTEIN LITHUANIA
LUXEMBOURG MALAYSIA MALTA MONACO
NETHERLANDS NEW ZEALAND NORWAY POLAND
PORTUGAL ROMANIA SAN MARINO SERBIA
SINGAPORE SLOVAKIA SLOVENIA SOUTH KOREA
SPAIN SWEDEN SWITZERLAND The People's Republic of China - HONGKONG
TURKEY UKRAINE UNITED KINGDOM UNITED STATES
VATICAN VIETNAM