The Tory are a nickname for the right-wing conservative party.

Historically it has been used in a somewhat derogatory manner. If somebody is a Tory then they tend to engage in more right wing policies than a Conservative who tends to be more center-right. Although technically there's no actual difference and they're all the same party.

Anyway they've lately started calling themselves Tory in a weird "let's take the word back" way, so you can more or less now just use the two words interchangeably.

Internally they have a lot of infighting about this, because some of the Backbenches (politicians who are members of the party but are not actually in government, think the equivalent of senators in the US) are unhappy with the parties direction because they feel that going full on lunatic right wing nut job might harm their chances of getting reelected. And based on current polling data it would seem that they are correct.