If I can define a thing, I can go after it. Clear definitions of spiritual realities open the door so I can pursue living by the Spirit. I choose to live and walk by the Spirit (Gal. 5:25)!

Logos is "the entire" while rhema is "a sub-component part"

Logos – The Greek word, most often translated “word,” means “the entire communication process.” One example of Logos is the Bible, the Word of God. We are to prayerfully meditate on the Bible, which allows God to speak to us through Scriptures, which in turn ignites our hearts (Lk. 24:32). The Bible also tells us to treasure or hide Scripture in our hearts so we do not sin against God (Ps. 119:11).

Rhema – This Greek word is most often translated “word” or "saying" and means "spoken word." The Spirit’s voice in our hearts is one example of rhema. Another example of rhema is when verses leap off the pages of Scripture and into our hearts, as this is the Holy Spirit speaking to us, applying the verse directly to our lives. In the Bible rhema refers to speaking, regardless of who is doing the speaking. It can be God, the Holy Spirit, satan, an evil spirit, ourselves or someone else speaking. In each case it is rhema. 

Rhema is a sub-component part of logos: Logos involves the entire communication process, which includes collecting my thoughts, reflecting on how I want to present them, writing them down, speaking them, and someone hearing and comprehending them. Rhema is just one part of this communication process, that being when the words are spoken. Rhema occurs as words leave one's lips.

• Never written - In this article which lists every reference in the Bible which has rhema in it, you will note that not one of these verses refers to written-down words. All but three times, rhema is referring to spoken words.
• A supernatural event - The remaining three times rhema is used, the text is noting God's supernatural actions. This brings to mind that one way God speaks is through supernatural events (Deut. 28:1-63; Isa. 45). If this is true, then supernatural events may be viewed as spoken words from God.
• For example - Acts 5:30-32 is an example of rhema referring to a supernatural event. "The God of our fathers raised up Jesus, whom you had put to death by hanging Him on a cross. He is the one whom God exalted to His right hand as a Prince and a Savior, to grant repentance to Israel, and forgiveness of sins. And we are witnesses of these things" (rhema). Note here that “things" is the Greek word "rhema” and it is referring  to the death, resurrection and exaltation of Jesus, which of course involves supernatural events, and is God speaking His mind about who Jesus is!

How God's voice, rhema, is sensed

Flow - God’s voice (rhema) sounds like flowing, spontaneous thoughts that light upon our mind (Jn. 7:37-39). The Holy Spirit is sensed as a river which flows within.

Naba - Hebrew word translated “prophecy;” it means “bubbling up.” So when I want to prophesy, I see Jesus present in the situation (Acts 2:25; Ps. 16:8) and ask for His thoughts and speak forth the thoughts and words that are bubbling up within me.

Paga - Hebrew word translated “intercession” – God’s voice leading me in prayer. The literal definition is “to strike or light upon by chance,” or “an accidental intersecting.” Spirit-led intercession is sensed as spontaneous thoughts that light upon my mind while I am praying. I honor these thoughts as they have been sent by God. So I fix my eyes upon Jesus, and tune to flow and pray, being guided by the flow (Heb. 12:1-2; Jn. 7:37-39).  

We live and walk yielded to God's spoken words flowing from our hearts.

• Yielded - "I can do nothing on My own initiative. As I hear, I judge; and My judgment is just, because I do not seek My own will, but the will of Him who sent Me" (Jn 5:30).
• To the Spirit - "If we live by the Spirit, let us also walk by the Spirit" (Gal. 5:25).
• Heart speaking - We speak that which we have been incubating in our hearts (Matt. 12:34).
• Power packed words - Death and life are in the power of the tongue, so we should be very careful about what we speak (Prov. 18:21).

The receptors in our hearts/spirits receive 

1. Ears of our hearts - receive flowing thoughts (see John 7:38) 
2. Eyes of our hearts - receive flowing pictures (see Acts 2:17)
3. Emotions of our hearts - receive flowing emotions (see Galatians 5:22-23)
4. Mind of our hearts - ponder and meditate (see Psalm 77:6)

Sensing God’s movement in our hearts can be called illumination, revelation, revelation knowledge, perception, discernment, word of wisdom, word of knowledge, or prophecy.

How YOU can easily reason together with God (Isa. 1:18) 

We begin by picturing the Lord at our right hand (Ps. 16:8; Acts 2:25). We ask Him for His thoughts on the situation we are facing. We put a smile on our face, relax and tune to flow, knowing that the flow within is the River of the Holy Spirit (Jn. 7:37-39). The flowing thoughts, pictures and emotions we receive flow from the vision being held before our eyes. When our eyes are fixed on Jesus, the flow comes from Jesus (Heb. 12:1-2). 

As we follow Jesus' pattern and yield our will and ideas to our Father's will, His ideas flow (Jn. 5:30). We are receiving and releasing words of knowledge, words of wisdom, prophecy, discerning of spirits, etc. (1 Cor. 12:7-11). We are walking and living by the Spirit.

One key safeguard is a multitude of counselors (Prov. 11:4). By two or three witnesses every fact and rhema is confirmed (Matt. 18:16).

Logos and rhema as defined in Kittle's Abridged Theological Dictionary of the New Testament

Please note how Kittle defines logos as the entire communication process, which involves collecting my thoughts, counting them up, reflecting on how I want to present them, writing them down, speaking them forth, someone hearing, comprehending and acting on them. Rhema, on the other hand, is a specific part of this communication process.

Lógos:

a. Like légō, lógos has first the sense of “collection.”

b. A second sense is “counting” with the nuances (i) calculation, (ii) account, (iii) consideration, or evaluation, and (iv) reflection, or, in philosophy, ground or reason.

c. Counting also gives the sense of “list” or “catalogue.”

d. We then find “narrative,” “word,” “speech.” In this sense, supplanting épos and mýthos, lógos acquires the most varied nuances, e.g., legend, proverb, command, promise, tradition, written account, conversation, sentence, prose, even thing.

Rhḗma: 

The root of rhḗma has durative significance. What is denoted is something definitely or expressly stated, i.e., “statement.” This may be an announcement or even a treaty. While distinguished as word from deed, rhḗma as an active word later comes to be used in grammar for the verb, and it lives on only in this sense.