Is it needed to install ssl certificate in host server?

if domain is added in cloudflare and proxy is enabled for the A records, then the Cloudflare ssl certificate installs on the domain so do i need to install the ssl certificate on the host server?
for example on tools like this, it will show that the ssl certificaet is of cloudflare,

so is it necessary to install ssl certificate on the host server? when accessing the website as well it shows secure and shows the cloudflare ssl certificate.

A server certificate is required on your origin so that Cloudflare can connect to you using HTTPS. (SSL/TLS mode Full (strict))

If you only allow Cloudflare to connect to you by HTTP, (SSL/TLS mode flexible) then the connection between Cloudflare and your origin is not encrypted. Your client will think their connection is secured (as it is between them and Cloudflare), but it isn’t all the way to your origin.

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what is the difference between full and flexible?

according to this

in flexible all connections between cloudflare and origin are http only?

while in full, the connection between cloudflare and origin can be http or https depending on how visitors visits?