While questions of infringement -- and definitely responding to a C&D letter -- are best addressed through counsel, it can be helpful for laypeople to have some idea of what's at issue before (or concurrent with) seeing their attorney. The ignorance about trademarks, not only among laymen but also among our brothers and sisters of the bar who don't practice in this area, can be astounding. So a forum like this can be very useful to help orient the layman to some of the complexities involved.
Some general information which the OP might find useful, e.g., is that the question will come down to whether or not there is a likelihood of confusion (in the market) between the earlier mark and the later mark. In assessing this, courts and the PTO look to not only what the names actually say but the "total commercial impression" of the marks. They don't have to be identical. Sound, meaning, look, can all come into play.
Also, the proximity of the goods is considered -- e.g., do they tend to run in the same channels of trade? Is one used for expensive goods where people usually take their time and think a lot about the purchase or is it some small item people buy on the fly? How likely are people to think the goods of one come from the same source as the goods of the other? One favorite example is DELTA for airlines and DELTA for faucets. Same exact name, but two different companies use it as their marks, without problem. Reason? Not likely people will think that the same company is in airlines and plumbing.
Then there's who has priority. The priority of the first mark depends on who USED the mark first, unless one of them has an ITU (intent to use) registration with the PTO, in which case they get "dibs" dating back to when they put in their application with the PTO.
So, e.g., if someone has a mark HANKERIN' for men's soap and someone else wants to use HANKY for women's toiletries, one could look at the fact that the names contain the same initial sound and look, "HANK...", and the senior user might complain that since the products all have to do with grooming and the two have a similar sound, the junior user should cease and desist. The response of the junior user, however, could be that the words although somewhat similar in sound give off vastly different commercial impressions. The word "HANKERIN" is a shortened gerund form of a slang verb meaning "to want" and brings to mind cowboy slang of rough and ready males; HANKY, by contrast, is the diminutive form of the noun handkerchief, connoting a small piece of delicate cloth associated with bygone days of women waving from trains, etc.
On the other hand, say I have a DOG brand cleaner and someone else starts to sell CHIEN brand cleaner. The words both look and sound very different from each other. Nevertheless, since the words both mean the same thing, only in different languages, there could be confusion. So CHIEN probably gets the boot.
The upshot of all this is to say that many factors go into the analysis. Do get yourself a good trademark attorney (and make sure they're experienced in trademarks), but also read up a bit on trademarks yourself. Searching this forum for "likelihood of confusion", "channels of trade", and "use in commerce" should bring up some good discussions.
Good luck.