There is no "defined term" for secondary modern (which no longer exist) or Senior Schools. Both of which you said were types of school.
Secondary modern schools today[edit]
Wetherby High School; a former secondary modern; now comprehensive school
In counties still operating a selective system, as of 2015 there were 130 schools fulfilling the role of the secondary modern by taking those pupils who do not get into grammar schools.
[16] These schools may be known colloquially (though not officially) as
high schools (Medway and Trafford),
upper schools (Buckinghamshire),
all-ability or
non-selective schools.
The term
secondary modern has completely disappeared in the naming of schools, although in 2013 the National Association of Secondary Moderns was founded by Ian Widdows, former Headteacher at the
Giles Academy in Boston, Lincolnshire.
[17] The organisation represents non-selective schools in selective areas
[16] and has organised a number of national conferences since it was founded, such as one in April 2016 addressed by Shadow Secretary of State for Education Lucy Powell, Tim Leunig from the Department for Education, and National Schools Commissioner Sir David Carter, among others.
[18][19]
In the state sector there are faith schools, free schools, academies and city tech colleges and that is it. (There may still be some state boarding schools too)
'High school' is a type of faith/free/academy. As is a grammar school.
You just said that grammar schools don't exist. Make your mind up.