Both carbamazepine and lamotrigine are listed as Na+ channel blockers. Carbamezipine's action is mainly associated with inhibition of postsynaptic neural activity, while lamotrigine is thought to inhibit glutamate release. Given that glutamate is the principal excitatory neurotransmitter in the brain, and if you insist of using a one-liner I would go for:
Both lamotrigin and carbamazepine can be said to inhibit glutatamatergic neurotransmission, albeit carbamezipine does so in a non-specific way.
My two most beloved drugs in one question!
First off, this answer is formulated from the perspective of both drugs being used as anticonvulsants in generalized tonic-clonic epilepsies. As anti-epileptics, Both lamotrigine (Lamictal) and carbamezipine (Tegretol) are listed as Na+-channel blockers.
Carbamezipine does so quite specifically, and it inhibits sustained repetitive firing by blocking sodium channels. It does so in a very clever way, as it only binds to Na+-channels of rapidly firing neurons, which is exactly what makes it a good anti-convulsant (Courtney & Etter, 1983). It also is believed to have anticholinergic, central antidiuretic, antiarrhythmic, muscle relaxant, antidepressant (possibly through blockade of norepinephrine release), sedative, and neuromuscular-blocking properties (Drug bank). Hence, your note that it increases the threshold for glutamate is true in the sense that it is likely to increase the firing threshold of glutamate-activated neurons.
However, note that carbamezipine (nor lamotrigine) does not increase the threshold for glutamate - glutamate has no threshold and hence it cannot be raised. It is incorrect word use.
Lamotrigine is also listed as a Na+-channel blocker, but the exact mechanism(s) behind its anti-convulsive and mood-stabilizing effects are unknown. In vitro pharmacological studies suggest that lamotrigine's inhibiting effects on voltage-sensitive Na+ and/or Ca2+ channels stabilizes neuronal membranes and consequently modulates presynaptic transmitter release of excitatory amino acids (e.g., glutamate and aspartate). It has also been shown to enhance K+ currents and GABA-ergic inhibition (Coulter, 1997). Hence, your note that it decreases glutamate release is correct.
Coulter, J Child Neurol (1997); 12: S2-9
Courtney & Etter, Eur J Pharmac (1983); 88: 1-9.