The "type of the term" is embedded in the term_t structure.

In file pl-fli.c:

int
PL_term_type(term_t t)
{ GET_LD
  word w = valHandle(t);
  int t0 = type_map[tag(w)];

  switch(t0)
  { case PL_ATOM:
  ...

with the type_map being an integer-to-integer mapping (i.e. tag to one of the PL_ values):

static const int type_map[8] = { PL_VARIABLE,
                                 PL_VARIABLE,  /* attributed variable */
                                 PL_FLOAT,
                                 PL_INTEGER,
                                 PL_STRING,
                                 PL_ATOM,
                                 PL_TERM,       /* TAG_COMPOUND */
                                 -1             /* TAG_REFERENCE */
                               };

The additional values PL_NIL, PL_BLOB, PL_RATIONAL, PL_LIST_PAIR, PL_DICT are deduced by content inspection

and those values defined in SWI-Prolog.h:

#define PL_VARIABLE      (1)            /* nothing */
#define PL_ATOM          (2)            /* const char * */
#define PL_INTEGER       (3)            /* int */
#define PL_RATIONAL      (4)            /* rational number */
#define PL_FLOAT         (5)            /* double */
#define PL_STRING        (6)            /* const char * */
#define PL_TERM          (7)

#define PL_NIL           (8)            /* The constant [] */
#define PL_BLOB          (9)            /* non-atom blob */
#define PL_LIST_PAIR     (10)           /* [_|_] term */

There are also PL_CODE_LIST (14) and PL_CHAR_LIST (15) as mentioned in PL_unify_wchars()).