I was learning a bit of model theory on my own and I faced a problem in understanding what an atomic formula is. I understood the meaning of term, which is
$(1)$- Every constant symbol and variable symbol is a term.
$(2)$- Let $f$ be any $n$- arity function symbol. And let $t_1,t_2....t_n$ be terms then, $f(t_1,t_2...,t_n)$ is also a term.
Let me know if there any mistakes in understanding of term
And using this we define atomic formula as,
(1) If $t_1,t_2$ are terms then, $t_1=t_2$ is atomic formula.
(2) If $t_1,t_2,....,t_n$ are terms and $R$ be any $n$ -arity relation symbol. Then $R(t_1,t_2...,t_n)$ is atomic formula.
Now I don't understand the condition $(1)$. What does '$=$' mean there?
Does it mean the general equal to sign we refer to or is it something else
No, here, it does not mean equality or terms (which would mean they are literally the same strings of characters). Rather, is a symbol which is interpres as equality, much the same as the symbol $+$ in the term "$x+y$" does not mean that we add terms (addition makes no sense for terms), it's just a symbol that is (typically) interpreted as addition.
For example, if $M$ is a structure and $t_1, t_2$ are terms without variables, then $(t_1+t_2)^M=t_1^M +^Mt_2^M$ and $M\models t_1=t_2$ when $t_1^M =t_2^M$. Both these things depend on the interpretation of $+$ – as well as other constant and function symbols occuring in $t_1,t_2$ – in $M$.