In fact, the emphatic consonants do not contrast with the pharyngealized consonants, since the latter are a subgroup of the former:
In Semitic linguistics, an emphatic consonant is an obstruent consonant which originally contrasted with series of both voiced and voiceless obstruents. In specific Semitic languages, the members of this series may be realized as uvularized or pharyngealized, velarized, ejective, or plain voiced or voiceless consonants.
[Italics is mine - Yellow Sky]
Traditionally, the Arabic ص ,ط ,ض, etc. are called pharyngealized and the Amharic ጠ, ጸ, ጰ, etc. are called ejective, although all the consonants of that kind in both languages can well be called emphatic, too, since emphatic consonants is an umbrella term for pharyngealized and ejective, or, in other words, pharyngealized and ejective consonants are just two kinds of emphatic consonants.
As for the physiological realization, the Wikipedia article on ejective consonants gives a pretty detailed scientific account of how they are produced, Wolf Leslau in his Amharic Textbook, 1967, p. 3, describes the mechanism in a simpler way:
The difference between the glottalized consonants and the non-glottalized consonants is best described as follows:
The non-glottalized consonants are pronounced as described above whereas in pronouncing the glottalized consonants, the stream of air coming from the lungs is shut off by closure of the glottis, and the air above it is then forced out through a stricture formed in the vocal organ. This stricture is at the lips for p̣, at the teeth for ṭ, ṣ, at the palate for č̣, and at the velum for q.
As you can see, he calls those ejectives “glottalized” and /p’, t’, s’, tʃ’/ are transliterated with an underdot, just the way the Arabic pharyngeals are often transliterated. The idea behind Leslau's description is that those consonants are pronounced by forcing out (i.e. ejecting) the air enclosed in the mouth cavity with closure of the glottis making a barrier on one side (hence the consonants are glottalized) and the “stricture formed in the vocal organ” making the second barrier. This way, it is not the lungs that push the air, but the muscles of the mouth, so there must be a noticeable break between the noise of the consonant and the sound of the following vowel.
Since in Amharic its ejectives are contrasted with the voiced and voiceless consonants, but not with pharyngeals, I think while speaking Amharic it is possible to use the Arabic pharyngeal /tˤ/ and /sˤ/ instead of of the Amharic /t’/, /s’/ as soon as your /tˤ/ and /sˤ/ sound differently from both /t/, /s/ and /d/, /z/ respectively. Nevertheless, there is still something which has to be done with the Amharic ejective /p’/ and /tʃ’/, since the Arabic language has no pharyngealized counterparts of those phonemes, it doesn't even have plain voiceless /p/ and /tʃ/.
UPD.: The Linguistics SE has a couple of questions with answers on how to pronounce ejective consonants:
• Good audio resources for the ejective consonants
• Can you give me some tips on how to pronounce ejective consonants?