There are many theories of what a "long consonant" is: here are the main theories. One is that every consonant has a "timing slot", which can be notated as C (vowels are notated as V), and a long consonant has two C's. This is the CV theory of Clements & Keyser. An alternative is that there is no difference between C and V at the level of the timing slot, everything is just X, and a long consonant (or vowel) has two X's. This is the X-bar theory of Levin (→Blevins). A version of this is Hyman's weight theory which has a single unit (he uses "x"), but with the special proviso that segments can merge under a single x, thus [pa] might start with two x's, but end up with a single x that both segments associate to. This then morphs into moraic theory, where vowels and some consonants are associated to a "mora" notated as μ, and a long consonant is somehow connected to a mora. The details of that theory are not particular uniform, because it doesn't handle long consonants in the beginning of a syllable very well, but there are a number of proposal. Morén's (dissertation) proposal is simply that "is moraic" is how you represent long consonants, but whether or not there is obvious "length", thus sometimes a final moraic consonant is said to be "long" and sometimes it is said to be just "moraic" (being moraic is the fundamental linguistic variable).
There is, incidentally, a potential for a contrast between a long consonant and two adjacent identical consonants, the latter often being called "fake geminates". Arabic is a language that has "real" geminates (a consonant is lengthened in a certain verb form) but also "fake" geminates, where a stem ends with /t/ and a suffix begins with /t/ so you get /t+t/. I haven't seen any evidence that the t-sequence /falat-ta/ or similar form is pronounced differently from a second-measure derived geminate. The question of whether, in some dialects, /falat-t/ "I escaped" is phonetically [falat] or [falatt] (in pre-pausal or pre-consonantal position, in a non-epenthesis dialect) is not clearly established, but it is plausible that there is a phonetic difference.